I had a small scratch on my old BlackBerry screen and putting a good screen protector on it did "heal" the scratch. I couldn't find it even when I was looking for it!
One other thing, when my watch had a scratch right across the crystal I made a paste of Bartender's Friend and water, and lightly rubbed it in a circular motion on the watch crystal. I then wiped it clean using a damp towel followed by one of those microfiber wipes made for eyeglasses. After that was done the scratch was gone. The final step was to put a polishing/buffing tool on my Dremel to polish the crystal. I don't remember which one I used, but I remember that it was safe to use on watch crystals. To this day I can't see the scratch on my watch. I got those directions from a Web-site about cleaning scratches on watch crystals, but I don't remember the specific Web-site.
I'm not necessarily recommending that for your iPhone---I have no experience with getting a scratch off of an iPhone screen---so take the story "as is."
Whatever you do, good luck. A scratch would make me crazy, which is why I put a screen protector on my iPhone as soon as I got it.