I’m pretty sure this wouldn’t count as counterfeit. It’s not meant to pass as real money. It’s gag money. You’re not required to tip though, so there’s nothing illegal about not leaving money or leaving something else instead. Obviously knowingly using counterfeit money is illegal regardless, but again this is counterfeit, just a gag.

If they knowingly pass a counterfeit bill, yes.

But this is a tip, not a payment so there’s no agreed upon amount that is supposed to be left.

Also, this isn’t a counterfeit bill, since it’s easily distinguishable from legal currency.

Is leaving a clickbaity political flyer in place of a tip a scummy thing to do? Absolutely. But it’s not illegal.