I had a similar problem, and wanted to share an alternate cheap fix. My 2 year old MBA screen was damaged by unnoticed juice splatter left between the keyboard and screen over night. I noticed a difference in reflectance next day, tried displex screen polish, but the damage became more noticeable! It was my successive applications of polishing chemicals that made the scratches more visible. So I would advise against that. The MBA screen is different and has a sort of film layer that can get peeled off by polishing solutions.
The fix that worked for me is to hide it with a screen protector! I had some success with a generic one called "6 pack anti-glare screen protector" for about 6 pounds. The acid damage was successfully hidden, even at different viewing angles. The downside is that you have to be really careful in applying the screen protector (my first attempt was a mess due to difficulty in aligning. I gave up, then restarted with fresh one from the remaining 5). My screen was left with small bubbles of trapped dust near the edge, but I settled because it already looked far better.
In retrospect, if my MBA had a screen protector to begin with, then I wouldn't have had this problem. But with a brand new screen and lack of skill in applying a protector, the screen would just have annoying little bubbles earlier...
I just realized that the screen protector, has a screen protector-protector (no instructions on a generic budget product). Peeling off the glossy plastic top layer reveals the actual matte screen protector. But that lessened the bubbles since most of them were between these two additional plastic layers. There are other types of screen protectors if you want to maintain the glossy mac screen finish, but I'm not sure whether they would be as effective in hiding scratches underneath. My mac screen now looks like a thinkpad's but the scratches are still hidden.