Okay, the quality isn’t very good but you can see this is the same joke, more or less, as the Abbot and Costello “Who’s on first” clip I put up before the holidays. The confusion here is between Peter’s name and the organisation People for the Ethical Treatment of Animals (PETA).
It shows how well-known the joke has become that Stewie considers it to be too common, saying, “Are we *really* doing this?”