use methanol/alcohol on a q tip first -use a rolling action to remove the black gunk as best possible..

it will still leave a mark on the screen, but this will be the best you cna do...only way to clean a screen correctly is to remove it and then wash it in detergent, followed by a final rinse in wetting agent..hopefully you can then get a dry screen (from my experience in camera repair I had a 60/40 success rate)..

And I'd forget removing the screen from a AT-1 - first you need to remove the top, then uncouple the wire that runs from the ISO dial to the shutter speed dial, then remove the main flex (without cracking it-a real problem on these as the flex is usually very brittle after so many years)..then remove the prism, and remove the screen form the prism....

Not a fun job!