Sounds like powdery mildew, which often comes when there is a lot of humidity. I don't believe it will hurt the fruit. I'd leave it to mature, even as the vines die.

Where do you live? How much time is left in your growing season?

George
Tahlequah, OK

i live in nebraska in lincoln and i should be good for atleast 2 weeks and probably longer some years i get tomatos and peppers upto first part of november so they will be fine on the vine here till atleast oct