Veneer is a thin piece of high quality wood laminated to a substrate (cheap wood or other). In Europe they did a thing called "veneer finishes", which consisted of a base coat and then a glaze coat which artisans could mimic almost any finish using feathers, brushes and combs with glazing compounds of various colors.
The answer to refinishing is to try very fine rubbing compunds, including tooth paste, if the scratch is not deep. There are wood refinishers who will redo, cracking or damaged surfaces. BTW Mercedes also laminates their wood to an aluminum backing to reduce any splintering in case of an accident.