"We have not started to eat yet."
The correct Klingon sentence is given as: wej maSopchoHpu'.
I think adding -pu' to this does not make sense. It is like saying that you have not completed the action of starting to do something. That does not make sense. It is enough to say you did not yet start the action. Just because something in English includes "have" does not mean that -pu' should translate it.
Am I not understanding this correctly?
The sentence is saying that our beginning eating is not yet a completed action.
wej maSopchoH We do not yet start to eat Our starting to eat hasn't happened yet. We are not yet in the midst of starting to eat.
wej maSopchoHpu' We haven't started to eat yet. The completion of our starting to eat hasn't happened yet. We are not yet at the point where the transition to full-on eating is behind us.
I doubt anyone would ever bother making this distinction; either sentence could be used more or less interchangeably in this instance. (That's not necessarily true of all uses of -choH + -pu', just this one.) Maybe imagine someone due to be at a special dinner calling someone who is already at that dinner. The caller wants to know whether he's missed the opening speech, which signals the start of the meal. The person at the dinner might say wej maSopchoH to indicate that the speech hasn't happened yet or wej maSopchoHpu' to indicate the speaker hasn't finished speaking yet (and possibly hasn't started, but that's not stated in the sentence). It's a bit of a contrived example, but that's what you get when you have to build these things out of zero context.