Puppets are a running gag in Invader Zim.
List Of Instances
For Probing Day, the Almighty Tallest told Invader Slacks to perform a puppet show depicting on how he plans to destroy the planet. Since Slacks wasn't prepared for this, he failed inspection and got a pummeling. The next Invader due for inspection, Invader Sqood , was more successful.
The Tallest created and operated marionettes of themselves to play a prank on Zim; even though the puppets were of poor quality (Tallest Purple's puppet's head fell off), Zim either fell for it hook, line and sinker, or simply chose not to comment on the absurdity.
Red has a boxing hand puppet of himself.