Screwed screws on the back case.

I do it all the time with a Dremel, using a small auger-type drill bit and just go for a few seconds at a time until the head of the screw cracks off. It doesn't take long & on the back cover (the one w 6 screws that holds the battery) there's nothing under there to damage it's high up enough off the m.board. There's nothing heat sensitive to damage under the gold screws on the m.board either, but still go in short bursts. NOW as for the top screen, I would only use the Dremel to out a stripped screw if it's one of the top 2, cuz the lower ones have fragile ribbons & the 3d controllers underneath (unless that's what you're replacing 😆).

*Another thing that works- if it's not in a recessed cavity- is just snap the head of the screw off with a pair of wire cutters.

And finally- if all else fails and it is a recessed screw- use a toothpick to apply a small dot of strong adhesive like jb weld or superglue, (recessed soldering is a bit impossible) to the screwhead ONLY, being careful not to let it touch the sides or get up under the screw > esp. once you squish something into it < Now Take your skinniest Allen key, or something similar you can turn (it won't ruin metal) and stick it in the glue. Use a thick book or box to hold it exactly upright. Let it set good long time 24 hrs. You've now molded a tool to turn the screw. Hope this helps!