My App has been rejected because of UIBackgroundModes

Question

We found that your app uses a background mode but does not include functionality that requires that mode to run persistently. This behavior is not in comp

Answer 1

You will not have to resubmit the app, they will respond to you.

https://developer.apple.com/appstore/contact/appreviewboard/index.html

This link will get you to the form for the appeal process, though I assume you have already done this based on info in your post. If you feel like you need an expedited review there is a link for that as well. You just have to make your case, try to be very careful to address every point they make about why your app doesn't meet the guidelines.