Wipe off the area containing the scratch with a rag. The area should be clean and free of dirt and debris.
Sand the scratch with a piece of super-fine sandpaper. Super-fine sandpaper is 360-grit or finer. Sand in the direction of the wood grain to remove the scratch without damaging the cabinet door finish.
Pour some scratch-removing polish on the rag. Rub the polish across the scratch. Keep working the polish into the scratch until the scratch disappears. Add more polish, if necessary.
Wipe off the cabinet door with a dry rag after the scratch-removing polish is dry. Follow the directions provided by the manufacturer regarding drying time, as it can vary between products.