iPhone 13 mini back glass: fingerprint-like mark that won't go away

My 13 mini's back glass has a mark akin to a fingerprint. It goes away when scratched with a fingernail. However, it's back very soon. Sooner when I use my MagSafe Silicone case. It is somewhat sticky. It feels like some sort of coating has worn off. I can always get the mark to go away, but it comes back again soon. Water and alcohol alike stick to the spot and drops don't roll on the glass like on the other areas of the back panel. This only appeared after I started using my $49 Silicone Case with MagSafe. Not impressed. Is there any way I can get it to go away permanently without replacing the back glass? Did a coating wear off or something? I also have some deep scratches on the front screen from the one time I put my phone in my pocket with my keys. That's another question, however.

Any help that doesn't involve replacing the back glass would be very much appreciated. I am a complete newbie and can't afford a laser machine. Thanks!