Wash the cabinets with a mixture of one tablespoon mild liquid dish soap and 4 cups warm water. Dampen a soft cloth with the soapy mixture and wipe down the affected cabinets to remove any grease, dirt or grime.
Dry the cabinets with a separate soft cloth and wipe down the surface with mineral spirits. This removes any remaining dirt and prepares the surface for the repair.
Sand the superficial scratches with 220-grit sandpaper. Gently rub the scratches with the sandpaper until they are removed. Wipe down the cabinet with a tack cloth to remove the sanding dust.
Apply two to three light layers of polyurethane. Dampen a sponge brush with the polyurethane and apply it to the previously scratched area to create a seamless finish.