When Bart has the two lizard birds, he goes to a bird meeting with Skinner, Apu, Moe etc. Before Bart enters the room, Moe rips up his card around his neck because of what Skinner said. Then, when skinner explains to Bart about the lizards, Moe's card is back around his neck. No sign of a rip.
Well actually he doesn't take the card from round his neck. Then he was in the background, where there would be less detail (unless there was something relevant, which Moe isn't).