There’s no religious tradition of a third monkey on Noah’s ark. The Bible says that Noah took fourteen (seven pairs) of all the kosher animals, and one pair of all the non-kosher animals. As far as I know, monkeys are not kosher.
I haven’t heard this quote, but certainly it’s pretty obvious what it means? It’s not referencing any known story, it’s making up its own story. Monkeys are thought to be some of the most intelligent non-human animals, so the joke is that maybe the monkeys knew that only two monkeys would be allowed on the ark, and all the rest would be obliterated.
