
Basically, I bought a new set of mechanical pencils (a white gum eraser is best, but my local store did not sell them individually) and began to run the scratches with the eraser in the direction of the scratches. Every few minutes, I would wipe the scratches with an alcohol solution pad to clean off the rubber residue (I saw guides online claiming that the alcohol pad alone would solve the scratches...they lied), then continue to rub the scratches "with the grain," so-to-speak, with the white gum eraser from the mechanical pencil. After about 20 minutes of rubbing on both scratches, cleaning off the rubber residue in between rubs, the scratches were GONE. Where I once actually felt deep scratches in the monitor, it was clear and smooth.
I have no idea exactly how or why this works, but many others online have had success with it as well. A lot of you might already know this trick, but I didn't and I swear it felt like Voodoo when I was done. I even fixed a few scratched monitors at work today as well with this trick. I hope this helps someone!