I'm only talking about the files specifically which contain the tilde "~" character.
Most skinners seem to leave them in there.
My usual hacky disclaimer: Based on my experience only, results are not guaranteed, proceed at your own risk.
I delete them, aggressively.
I also delete the reimport.lst file which is usually in there.
I also delete the TmpPngs folder if it's in there, which it usually isn't.
And In what way does this affect that the skin doesn't work on 7 ?
I honestly don't know, but I would expect "None".