If a user is making a good but incomplete edit, I do not think we should "punish" them by rejecting it. We want to encourage them to become better editors, not discourage them from editing at all.
So how about instead showing the original editor a message similar to the rejection message, when their edit was improved? They could then click through to the improved edit, notice that your improvement also removed the "Thanks", and learn it that way.
There could also be an "improvement reason/message", where you can explain to the original editor why you think it had to be improved.
That way, you can still teach them how to improve their editing, without rejecting an edit that, while incomplete, still improved the quality of the original post.
I think constructive feedback is a better teaching mechanism than just a plain "no, not good enough!".