They spin but the metal threaded part spins with the screw which is the problemEven if you get a new try, the risk of damaging the housing would remain. Not done this personally but can think of two options.
If the screws were stuck due to over tightening, there’s a bunch of screw out kits that go for $5-$15 that can help. Be careful not to use too much force as it could break the plastic pieces.
Another solution might be using a penetrating oil for rusted parts. Hammering a screwdriver can also help. Check this article:
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The battery cover is actually good, I’m not sure where that random piece of plastic came from. My only guess is the previous owner tried to use it as a washer or spacer for whatever reasonGrab them with a pair of vice grips. Looks like you are buying a new battery cover anyway, since there's chunks of it underneath those bolts.
-Mike