Photo is not sharp enough to be certain of damage. Find someone who knows how to French polish shellac. Main way to make repairs unnoticeable is to restore a flat surface for light reflection. Process described below removes no wood. Scraping and sanding only removes shellac.
Top mark looks like a dent (compressed wood). Bottom mark looks like there could be some gouging (torn wood fibers) into the tint/stain. If tint is removed than that is a separate fix. Same repair method for dents. Spot remove shellac by alcohol dissolution. Steam to remove dents. Drop fill any remaining depression with platina or super blond shellac. Scrape and sand (400 and 800 wet/dry with olive oil) to level. Polish area with a few coats of same shellac.
Top mark should be 100% unnoticeable. Bottom mark 90% or better.
Photos show repair of 130-year old shellac with drop filling in areas of wood loss. Some smart guy thought wood putty would be a good repair.
