Removing Scratches out of Glass
Historically, deep scratches cannot be removed, light scuffs can be polished out of the glass using a glass polishing kit sold by the Eastwood company, but not actual scratches with a depth to them.
Here's a related article,
What it means to remove a scratch out of anything...
In order to remove a scratch out of anything, metal, plastic glass, paint, etc. You must remove material around the scratch until the surface is level or equal to the lowest depths of the scratch or scratches.
The below diagram if for paint, the the same thing applies to just about an surface material or coating.
"In essences, you don't really remove a scratch, you remove material around a scratch."
Then the big question is, is the material or coating workable, as in can you abrade small particles of it and leave behind an original looking surface. For example, some things you can abrade, (remove the scratch), but you can never completely remove all of your abrading marks, thus you can't really fix the problem, all you can do is exchange one set of scratches of a different set of scratches.
The next questions is, how thick is the surface material you're working on or the coating. You are limited to what you can do by the thickness of these to things, (surface coating or surface material), and whether or not this surface is workable.
Sometimes you don't know what you can so until you try. It's always a good idea to test your choice of products, applicator materials and application process, (By hand or by machine), to an inconspicuous area. If you cannot make a small area look good with your product, applicator and process, you will not be able to make the entire surface look good. It's always a good idea to test first and error on the side of caution, versus make a mistake you cannot undo.
The only product out on the market that we know for removing light scratches in glass is made by the Eastwood company.
Do a Google search using the words Eastwood Company and you should be able to find the kit.