How can I repair a scratched MacBook Air screen? (A1369)
The protective plastic cover on the screen is bonded to the complete LCD display and not really removeable as a single element. A video on Youtube ("A1369 13.3" Macbook Air LCD Screen Repair step by step howto guide") explains the removal and disassembly of the display and is one hour long. It involves a heat gun and very careful use of special tools:

 

Conclusion: there is no way to remove the single element (scratched screen protector) in a simple procedure. It would be probably easier to replace the complete lid assembly, but this items costs 500 USD / 440 EUR (Summer 2015). This seems excessive for a screen which has "only" a few very unattractive scratches.

Mental note for next Mac: always place a protective cloth between keyboard and screen.