Sometimes the only thing keeping you from buying a pair of glasses is the manufacturer's logo or perhaps the former owner's monogram. Many glasses are marked with a laser. Laser engraving only affects the surface of the layer. You can easily remove the laser engraved markings on either metal or plastic glasses with sandpaper. Purchase the items you'll need at a hardware or home improvement store.
Wash the glasses with soap and water until they are completely clean but not dry.
Lightly sand the area of the glasses with the mark. If you press hard on the glasses you may scratch them or sand off too many layers of plastic.
Spray the glasses with water to keep the area wet while you sand it. This will also remove the plastic debris so that you can see when the mark is removed.
Run clear water over the glasses once the laser engraved mark has been completely removed.
Dry the glasses completely with a microfiber cloth. Do not use a paper towel, as that will leave paper residue on the glasses.
Wash the glasses with soap and water and dry them completely with a microfiber cloth.
Lightly sand the mark with silicone carbide or metal sandpaper. Do not apply too much pressure.
Run clear water over the glasses when the mark has been completely removed. Dry the glasses completely with a microfiber cloth.