Etching on polycarbonate signage?

Anyone got any clue at all on how to remedy etching on what appears to be polycarbonate sheeting with some sort of coloured film over it? Have a feeling it’s a lost cause but would like to come back to the client with something constructive…

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Have a sign company put a matching blue vinyl over it


I guess almost anything is paintable, but client is worried about it looking professional afterwards.

I got the impression the sign company weren’t in for being helpful and only wanted to disassemble the sign and ‘dip’ the sheet in whatever it was they put it in the first time, but that is a good suggestion, thanks.