How about renaming the "needs improvement" flag?
The current name is simply untrue for a number of questions that need to be closed. No amount of improvement is going to turn "What's your favourite programming joke", or a question that belongs on another site, into an appropriate question.
My suggestion might be "not a good fit". "Not suited for [Community]" could also be a consideration. Based on new the close dialog phrasing, this only matches the phrasing of a subset of the close reasons, but in reality it could apply to the other reasons too. If we make it roughly match the close dialog title (which is arguably the most logical approach), that would mean making it "should be closed" or changing the close dialog title.
The description can largely stay the same, apart from a minor addition for the above.