How can I repair a scratched MacBook Air screen? (A1369)

I have a mid-2011 **MacBook Air** (model A1369), 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. The screen is *not* protected by a glass layer – I hope it has a removable user-facing **plastics film**. Is there a way to **replace** the **scratched layer** of the screen assembly to get rid of the scratches? I feel confident to do repairs myself and have done similar things in the past. Here is a sketch of the scratch areas: This picture is based on a photo. The scratch shapes are correct, but color and intensity are exaggerated for readability.