…and what about Smite a Card from Olympus Fluxx?

A: The answer is that when you pick an Action card to go onto Let’s Keep Doing that, it’s like they become grafted together, so you can’t do anything to one without affecting the other. In this case the Action is really just a reminder, sort of a “shadow card” that indicates the current power of Let’s Keep Doing that, which is the Rule which is actually in play, and the Action is not considered to really be “in play”.

So we would rule that you can’t actually zap Zap A Card, you could only zap Let’s Keep Doing That. When you zap Let’s Keep Doing That, the applicable Action would go in the discard pile, and, as per the Zap A Card instructions, the Rule would go into your hand.

With Smite a Card, the only difference is that BOTH cards would end up in the discard pile: trying to smite Smite a Card itself would end up smiting Let’s Keep Doing that, and it would go in the trash.