According to technology and culture website Geeks are Sexy, there are a couple of different techniques that can be used to remove scratches from a PS2 disc, including using a mild abrasive substance, such as Brasso metal polish, and even a banana. The site also recommends the SkipDr DVD and CD Manual Disc Repair System, though metal polish and bananas are both less expensive and more readily available.
Apply a small amount of metal polish to a cotton swab and then gently polish the back of the PS2 disc in small, circular motions. Once the scratches disappear, rinse the disc with water, dry it with a clean cloth and insert it into the PS2. Metal polish can emit irritating fumes, so be sure to clean the disc in a well-ventilated area.
Alternatively, use a banana and a bit of glass cleaner to remove minor scratches from a PS2 disc. Simply cut off a small piece of the banana and rub it on the back of the scratched disc in a circular motion. Then use the banana peel to wipe down the surface of the disc.
Next, wipe the surface of the disc with a clean cotton cloth in a circular motion, being sure to apply moderate pressure. Finally, spray the back of the disc with a bit of glass cleaner and wipe it clean.