I think Roxy54's advice is right on target. I got into a legal battle w a mover, who presented me with a bill that was 3X the estimate. Yes, triple. When I balked, they drove off w all of my worldly goods. It cost me $1K in legal fees to get my stuff back; I still had to pay the bastards 110% of the estimate, AND of course they demanded a release on any damage. And I got lucky, because the estimate was on an interstate form that had a stipulation for resolution of billing disputes. I'm sure that there are lots of reputable movers and lots of people who try to stick movers for pre-existing damage.
But, sometimes you gotta suck it up and write it off! Now that doesn't mean you shouldn't present the mover with a repair estimate. They will counter by saying that they will have their guy do the job. He will come out and rub a little almond stick (or even half of a walnut) and/or some dye with a Q-tip, show it to you in some dim interior light, and say "TA DA!!! All better!!!. Then you will have to wait a day or 2 for the almond stick to dry out, put it in some good light and take a picture and tell the mover, nice try. He will probably say "Sue me!. Then you have to decide if it is worth it. If you think you might go down that road, you will need to document everything in writing with pictures. Send registered letters, not email. Most likely you will end up in small claims court. The best you will do, most likely, is get the repair cost. There's a good chance the mover will not even show up. So you win a default judgment. In most/maybe all states, you will have to hire a constable or process server or sheriff to serve the judgment papers. Then when they don't pay, you will need to try to find out where they bank, identify the proper corporate entity, and ask the court to order the bank to pay you. Then you'll probably need to get another process server to get that to the bank. Fees all along the way. $25 here, $100 there. Lots of lost time and aggravation. Unless they are totally destroyed, Roxy54 has probably nailed it.