Are they scratches or cracks? Big difference.
I had a few thin, semi-deep scratches on my screen a while back. I put a dab of white, semi-gritty toothpaste on the scratches themselves, and buffed it into the scratches with a dry towel corner until all residue was gone, then repeated. Did it about 4-5 times and lines were almost entirely buffed out. Can no longer feel lines and can only see when looking extremely close for them. Phone smelled good to boot! Haha!
Cracks... that's a whole another issue.