The real ques is how much it will cost to get it fixed. They can fix it even if they have to replace it, but at what cost? Is the $20 worth finding out what it would take to repair it or would the money be better spent toward a new servo?

If this had been hooked up backwards only a few moments, I'd be sending it in, but running it wired backwards long enough to get it very hot likely compromised the electronics at a minimum.

My bucks would go toward a new servo and chalk this one up to a lesson learned.