Scratches in glass are quite easy to buff and polish out with a $20 Wal-mart high speed rotary tool. All you need is the little 1" round sanding disc kits that include the mounting wheel/pad and discs that can be gotten from Ebay or Amazon for cheap. Try to get one that has 1000 grit, 3000 grit, and 5000-7000 grit discs. Then you need a small amount of cerium oxide polishing powder.
You simply start with 1000 grit, which will take material off to level the scratched area. You will see the glass dust flying off the scratch edges as you lightly hit the glass. When you cant see or feel the scratch you will be left with a permanent smudge/blurry spot. Go over that spot with 3000, then 5000-7000, it will become less smudgy. Finally, some cerium oxide water slurry with a low speed drill or a damp rag using circular motions (this works just as well). The scratch will be gone and the glass will be just as glossy and shiny as it was new. Its very satifsying, actually.
Now-- just make sure there is no film or anti-glare coating (its usuallys a blueish color) on the screen before you begin the process. If there is, you would need to remove it first. It it just appears as clear glass, you should be good to go!
**Edit-- this actually looks extremely light. I would first hit it with 7000 grit to see if it simply disappears. If not, try 3000 or possibly 2500 if that doesnt work. If it disappears but leaves a "greasy" look, work your way back up with 3000, then 7,000, then cerium oxide slurry with a damp rag. It sounds like a lot, but its really, very, very easy. Hit back if you need more help.