Cleaning ‘staining’ off bottom of MacBook screen
I've encountered something similar before and from the looks of it, the glass/plastic coating is etched.

A user once tried to clean their screen with acetone (nail polish remover) and it physically damaged the glass coating.  In the pre-Retina days, the glass was replaceable so it wasn't a costly fix.

Unfortunately, for the 2015 models, the glass and LCD are glued together so you will need to replace the entire assembly. 

IFixit.com has an excellent guide on replacing the display assembly.  It's not difficult, per se, it's time consuming and you must exercise a good bit of diligence (it's not something you going to speed through) when disconnecting the components as they can be damaged.  If this is not your cup of tea, have a pro do it for you.  Read the guide anyway, this way you know what to expect of the tech that does the work.