The coating wouldn't have anything to do with it scratching. If anything...the coating would probably help prevent scratches as you now have a polymer OVER the screen.
As someone else said, maybe there's a scratch in the coating.
And yes, you could possibly get the coating off with a solvent such as alcohol, which would eat away at the coating.
I don't know how good of an idea that would be, as it would probably take quite a bit of effort to get it out. Have you tried buffing it with just an LCD cloth to see if it smooths out?
From what I see, that coating is pretty much bonded to the screen, so getting it off would probably be a task, but having taken several chem classes, alcohol will slowly eat away at any polymer, but it probably won't do it quickly.
I think that's why apple changed the cleaning directions for the 3G S. They used to tell you with the 1st gen and the 3G that you could use a lightly damp cloth, with the 3G S they tell you to use a dry cloth, nothing wet. I'm pretty sure that's why.