Bluff the Eavesdropper

"When a spy finds a listening device, the last thing he does is turn it off."

—Michael Westen (Narrator), Burn Notice

People notice their phone is tapped, or see a microphone in their potted plant, or otherwise discover that someone is spying on them. So they start acting.

A specific version of this is when two people being audio bugged carry on a conversation for the benefit of the bug while holding the real conversation by sign language or exchanging written notes. (And the visual conversation will often begin with a note or signal meaning "I should warn you we're being bugged".)

Can be used as Number 33 of The Thirty-Six Stratagems. Compare Feed the Mole.

Examples of Bluff the Eavesdropper include:

Anime and Manga

Sasuke did this in Naruto by giving his teammates a password that the real Naruto would never be able to remember. The imposter Naruto who showed up did remember.
Combined with Bluffing the Murderer in The Kindaichi Case Files: On at least one occasion, Kindaichi stages a fight and pretends to go off alone in order to lure out the suspected killer.
In an episode of Ghost in the Shell: Stand Alone Complex, the Major realizes that the Tachikomas are observing her meeting with Batou. She and Batou proceed to hold two conversations simultaneously: they speak audibly to mislead the Tachikomas, while using their neural implants to message each other wirelessly and say what they really mean.
Fullmetal Alchemist: Hawkeye needs to get Mustang a message about the identity of the homunculus Pride, but knows that Pride is observing her, so she signals Mustang by tapping her mug. They then have a long, apparent innocuous conversation that's a cover for a coded message.
Light did this with Kyomi Takada in Death Note: They were having one conversation for the benefit of the Task Force listening in, while secretly writing notes to each other containing the real conversation.

Film

Kentucky Fried Movie segment "A Fistful of Yen". While in Dr. Klahn's headquarters, Loo is about to discuss escape plans with Ada Gronick when she shows him a listening device. They make polite conversation as she shows him the rest of the devices and spies.

Ada Gronick: [speaking quietly] The guards will have to be bribed. We'll need money.
Loo: We can raise the money, that's no problem. [Reaches up and pulls down an overhead microphone, speaks into it] But that would be wrong.

The Adventure of Sherlock Holmes Smarter Brother. Sherlock Holmes and Watson are in a room when Holmes silently informs Watson that there's someone listening at the keyhole. They then have a conversation intended to fool the eavesdropper that they're leaving the country.
The villains do this to Dick Tracy in the Dick Tracy movie.
In the movie The Guns of Naverone, the team is going over the plan when one of the main characters hands to the other a note that reads keep talking. The rest of the team keeps talking while Stavros sneaks over to the door catching the eavesdropper and pulling him into the room. It's the first sign that things may not be going as planned.
In After the Sunset, after the retired jewel thieves discover that the FBI agent has hidden a bug in their apartment, they begin talking like they're getting ready to have sex. (the fact that he's eagerly listening to all this is genuinely creepy). Then the woman claims to have invited another woman over to join them. . .the agent's mother.

Literature

Used in The 39 Clues series, more than once to throw the other Cahills of the track
During the "David" arc in the Animorphs series, once the team realizes how unstable and dangerous David is, they sometimes do this while discussing their plans, in case he is eavesdropping on them in morph.
In the Discworld books, Vetinari sends all his semaphore communiques using codes that are "fiendishly difficult" but not unbreakable. He wants people to read them so that he knows what they think he thinks they're thinking.
In one of the Foreigner novels, protagonist Bren is in a situation where, to communicate with the alien atevi, he must use the communications systems of a group of humans who are not only eavesdropping on him, but blocking the transmission of anything they don't like. To get around this he sends a message comparing his situation to a scenario in a particular genre of atevi popular culture, a comparison which seems innocuous to the human eavesdroppers but which clearly explains exactly how much trouble he's in to any atevi.

Live-Active Television

In Farscape, Crichton and Aeryn eventually do this to Scorpius, apparently getting him to believe that their relationship is at an end and Aeryn can't be used against Crichton. "Apparently" being the operative word; Aeryn ends up getting kidnapped in an operation that Scorpius apparently had a hand in, so the whole gambit is rendered completely pointless because Crichton ends up offering Scorpius everything he wanted in return for Aeryn's safety.
In Burn Notice, Michael often does this when he knows he is being bugged.
This was done in the season 3 finale of The Mentalist, to give one of the CBI employees who might be Red John's spies the room number of a person they were hiding. The person is actually somewhere else, and the room number is a trick to reveal who is Red John's spy.
In the Doctor Who story "The Two Doctors", the Doctor gives some key exposition to his companion and is overheard by one of the villains, but he later reveals that he knew the villain was listening and sabotaged his exposition accordingly.
Hogan's Heroes: Hogan finds out that one of the new prisoners of war is actually a German spy, so they pretend to trust him and tell him they're going to take him to their secret hideout blindfolded. They then let some false information slip out while talking and make noises that imply their hideout is under the watertower.
- In "Eight O'Clock and All is Well", a Mole uses the technique against them. As far as the Heroes, listening through a bug in Klink's office, are concerned, the new prisoner is playing Klink to get out of a punishment. Meanwhile the Mole has passed Klink a note identifying himself as Gestapo, and is pouring Klink a drink.
Seinfeld: While in the diner waiting for a reporter who's going to do a story on Jerry, he and George notice a young woman eavesdropping on their conversation, so to mess with her they pretend to be gay for each other. It turns out that she's the reporter Jerry was waiting for, who then outs them in her school newspaper as gay. They try desparately to convince her that they're not gay -- Not That There's Anything Wrong with That.
In one episode of Scrubs, Dr. Cox realises that Doug is listening to him and says to himself;

Dr. Cox: If this kid[Doug] doesn't leave I'm gonna kill him!
Doug: ... *begins to leave*
Dr. Cox: Hey, if you leave, I'm going to know that you were listening to me and kill you anyway!

In one episode of Sue Thomas FB Eye, the characters play football. The other team hides their mouths during huddles so Sue, who is deaf, cannot read their lips. On the final play, they let her see their lips, but call a fake play. She doesn't fall for the bluff.
Played With in an episode of Babylon 5. Londo discovers a listening device in a bag of groceries from a Drazi grocer. He spends a few moments saying several insulting things about the Drazi ambassador's wife under the pretense of not knowing he was being recorded, before smashing the bug.
While posing as a spy couple in NCIS, Tony and Ziva have (simulated) sex because they know the room is being filmed.
In the climax of the Star Trek the Original Series episode "The Deadly Years", due to having been rapidly aged by mysterious radiation and gone senile Kirk has stepped down from command and his incompetent replacement has led the ship through the Romulan Neutral Zone and the latter are about to destroy them. Suddenly a cure is found, a restored Kirk appears on the bridge and gives an order to relay a message to Starfleet... using a code previously established as having been broken by the Romulans, which briefly causes the crew to wonder if he's still senile. Nevertheless, they open the channels and Kirk sends a message that the Enterprise will self destruct via the Corbomite Device and destroy any ship in a huge radius. The Romulans intercept the message and leave.
White Collar: Fowler is tapping Peter's phone, so Peter pretends not to know that his cell phone is also bugged and uses it to call Neal so they can feed Fowler false information.
On All My Children, a villain has bugged his girlfriend's house, suspecting (correctly) that she's on to him. Luckily, she finds it and proceeds to sing his praises to everyone.

Newspaper Comic

Doonesbury: While Zonker is being kept in a hotel awaiting trial for possession of marijuana, Mike finds a bug under a lamp. The two start very obviously acting, talking about how completely sober Zonker is in order to tip off the prosecutors that yes, they know there's a bug in the room. It gets the case thrown out of court.

Theatre

Used in Much Ado About Nothing to make Beatrice and Benedick fall in love with each other.

Video Games

In Metal Gear Solid, Liquid and Ocelot discuss their PAL codes and Snake's card key deactivating Metal Gear Rex, knowing that Snake is spying on them, to further fool Snake into unwillingly doing their bidding for them.

Webcomics

Xkcd #525:

Now and then, I announce "I know you're listening" to empty rooms. If I'm wrong, nobody knows, and if I'm right, maybe I just freaked the hell out of some secret organization.

In Questionable Content, Faye, Dora and Marten against the Vespavenger, starting here.

Western Animation

From Avatar: The Last Airbender: a masterful example by Azula, when she has Mai and Ty Lee purposely reveal that they're Fire Nation in disguise... to the pair of Dai Li agents they knew were eavsdropping, overhead. She knew they'd ferry the news back to Long Feng, and knew he couldn't resist the opportunity to use it against her. So she wasn't surprised when those same agents brought her to his cell, where he coerces her into helping him under threat of exposing her to the Earth King. Azula "reluctantly" agrees. It doesn't end well for Long Feng.
In one episode of Gummi Bears, the king tries to find out a famous chef's secret recipe by listening at the door, which the chef thwarts by reciting absolute nonsense instead of his ingredients. However, this does not thwart Cubbi, Sunni, and Tummi, who are hiding in the kitchen and can write down the actual steps he's taking.