I think here he is thinking of "finish" in the sense of "finishing off", not in the sense of "finishing up with". He is not wishing for Israel to "solve" the issue, he is calling for them to kill all Palestinians.
I think it's supposed to be vague enough that they can tell "moderates" it means "finish the conflict" but the MAGAs understand it as "final solution."
I don't think he walks in there with notecards, no. I think he's in the habit of trying to talk like Stringer Bell about things after decades of being a modestly successful white collar criminal. I think that at this point answering questions with vague phrases isn't a conscious strategy so much as just part of who he is.
The quote is "You have to finish the problem,".
English is inexact but it seems clear to my reading that Trump means exterminating Palestinians or at least Hamas.
It's just an awkward rephrasing to avoid the words "final solution", which is what he really wanted to say, but that's still a bit too mask off for now.