Sand the scratch with sandpaper to smooth away rough edges and the uneven surface of the wood paneling.
Oil the sanded area to restore the finish. Wood or floor polish are acceptable products for wood paneling, although petroleum jelly and cooking oil are household items that work well in a pinch.
Conceal the scratch with a putty stick. Choose a stick in a shade close to or matching your wood paneling, and rub it over the scratch until the scratch is filled.
Run the edge of a putty knife over the filled scratch to smooth out the putty in the scratch. Wipe away excess putty with a clean, soft cloth.