Just moved in with my girlfriend and I want to replace the overflow drain cover but the old screw is completely rusted and I can’t get it out. Is this something that I can resolve myself? Or do I need to call someone? Best resolution I’ve come up with is using a drill with a small bit to drill into isn’t and then gradually up the but size, but worried about damaging it beyond repair.

https://drive.google.com/file/d/1JicpJsi9cR9lnk_6YB7A0m2pJ5NODz88/view?usp=drivesdk