Wipes are paper-based I believe, and paper is slightly abrasive.
This is typical of micro-scratches, which appear to circle around a bright reflected light (aka "swirls").
Apple says:
"Use only a soft, lint-free cloth. Avoid abrasive cloths, towels, paper towels, or similar items."
"Dampen a soft, lint-free cloth with water only, then use it to clean the computer's screen."
I don't think there is anything you can do, sorry. I suppose you can try the damp soft cloth in case they are residual marks and not micro-scratches. It is possible to buff them out a car's clear-coat (for example), but this would ruin the anti-reflective coating on a computer screen.