I used cream for my itch...... sorry ETCH!!
Well etching is a type of abrasive (much like my itch) so to remove it you'll have to use some sort of cream (like my itch) that abrasive enough to remove it but soft enough to make it look like polished perspex.
Be easier quicker and less labour intesive to get a new window and it'll look good too.
You could just buy some more perspex and replace the payne?
TBH if u dont like the etch, replace or sell the case.
Anything less than that will not give you the results u desire.