The finish is only a few thousandths of an inch thick. The depth of the damage will have quite different requirements for a fix.
http://www.popularwoodworking.com/article/Repairing_Color_Damage/
Another way to fill scratches is to get some lacquer. Fill a paper cup about 1/2″ deep. Let it sit out for a few days until you have about half the volume or less. You will have a very thick, syrupy lacquer. Using a toothpick, drip and drag lacquer into the scratches. Let it flow out and dry. Sand to level. Repeat if needed. You may need to spray a little aerosol lacquer on at the end to match the sheen. You might also apply the aerosol after dropping in the lacquer to get it to flow out and level.
As with all new procedures, try this out on a practice board first.