As before, a clean rag made from cotton or microfiber is ideal. You can use a cotton swab instead. Rub the toothpaste over the scratched area. Always move from the center directly to the edge. Repeated movement will slowly wear down the CD, smoothing it out to the level of the scratch. Do not press hard. Hold the CD under running water. Wipe it with a clean cloth in the same direction of movement. Be careful, as  dry CD is more easily scratched than a wet one. Blot away most of the water first, placing a lint-free cloth directly onto the CD and lifting. Finish by air drying or very gentle rubbing with a dry area of the cloth. As always, rub from the center to the edge in straight lines. Test the CD once it is completely dry. If it still doesn't function, you can try the same cleaning process with a polish meant for silver, plastic, or furniture. Never use a polish that smells like kerosene or contains petroleum derivatives, as these can break down the CD.

Summary:
Squirt the toothpaste onto a lint-free cloth. Gently wipe the scratched area. Wash off the toothpaste. Dry the CD. Try stronger abrasives.