How can I repair a slightly scratched MacBook Air screen?

I have a mid-2011 MacBook Air, whose screen has attracted some unsightly but superficial scratches. They look like smudges, but I suspect a layer of coating (or similar) has come off.

Most likely, the scratches stem from frequent transport with the screen pressed to the keyboard.

Here is a sketch of the scratch areas:

(Based on a photo of said screen. Shapes are correct, but color and intensity are exaggerated for readability.)

I hope the screen has a user-facing plastics film or layer.

Is there a way to replace (parts of) the screen to get rid of the scratches? I feel confident to do repairs myself and have done similar things in the past.