How do I release a screw whose head is flush with the surface and the notch is so worn down that the screwdriver can't make contact?

Sometimes I have had success re- tapping the head of the screw. Using a hammer and screwdriver like a chisel.

Also a but of wd-40 under the screw helps.

I should add, the screw and surface next to the head seem almost molded to each other. There is hardly any room between the edge of the screw head and the screw hole.

Drill out the screw. You’ll need a bit that’s marked “HSS” (high-speed-steel) on the shank, and at least as large in diameter as you think the threaded portion of the screw is.

The idea is to drill straight down through the center of the screw head (a drop or two of oil will help the drilling). Use moderate speed and firm pressure. As soon as you’re down to where the screw head joins the shank of the screw, the head will separate from the shank and the cover will be freed.

Even if you don’t hit the center of the screw dead-on, the head will still only be attached by a small bit of steel, and will be easily broken if you pry up the cover.

Edit: Actually, a screw in a drain cover would likely be brass. If so, just about any drill bit would do the job.

@Harp GA-I need one of those bits!

Similar to what @Harp suggests is to get a screw extractor bit—basically a drill bit with the threads running in reverse. You drill into the head in reverse, the bit drills down into the screw and starts turning it from the inside out—then you don’t have worry about prying or anything. I’ve had great success with these for screws that have been totally stripped.