Pickup screws stuck... what do?

Back the screw off as far as you can using a flathead screwdriver if a Phillips won't work, then grasp the head with a pliers and twist counter-clockwise.

 

Last time I ran across stripped pup height screw head I found it easier to use the pliers sideways at first. Though that only allowed for very small turn each time. Once I got it loosened a bit was able to switch to pliers applied from above. Needle nose pliers might be easier to use to. Try very gently wiggling the screw then slowly and carefully try to unscrew it.

 

If the head of the screw breaks or twists off, then you can buy one of those nifty extractor bits for any normal drill.