I had this same problem with my Model S years ago. I held the screw anchor from rotating with a small awl while I unscrewed the screw (as shown).
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With the license plate removed and the trunk fully up, I applied a few drops of Superglue to the screw anchor while slightly rotating it back and forth with a flat screwdriver to spread the glue. 5 seconds later the anchor was solid. Doing it with the trunk fully up stops the glue from running.