Sand the scratches with your extra-fine sandpaper, using light, quick strokes to degloss the surface in and around each scratch. Don’t sand into the wood itself; just dull the gloss. Wipe off the dust.
Scrape wood putty over the scratches with your putty knife, running the flat end of the knife perpendicular to the direction of each scratch, so the putty fills each one. Wipe a cotton cloth over the area to take up the excess putty, leaving it just in the scratches.
Let the putty dry for 10 to 12 hours. Sand the area lightly, removing any residual putty. Wipe off the dust.
Use your foam finishing brush to spread a light, thin layer of polyurethane over the area. Let it dry for eight hours. Lightly sand it, brush off the dust and add another layer of polyurethane. Let it dry for 12 hours.