Sellers or Movers damaged hardwood floor after final walkthrough!

[Matt Morgan]

Final walk through was Tuesday 11-5. No damage to hardwood floors at entrance of home on Tuesday 11-5. Sellers movers removed all belongings on Wednesday 11-6. I closed on my home on Thursday 11-7. We moved in Friday 11-8. 
Realtor met met at the house and did a walk through a few minutes before we arrived. She immediately notice 2 large deep scratches on the hardwood floor. This area is 90 sq ft. The scratches are on beveled hardwood floor. The scratches run approximately 22 inches long and there are 2 of them. Looks like movers dragged a filing cabinet across the floor.

I received a quote today to fix the issue. Due to the beveled edges being a 1/4 inch it is extremely difficult to sand this down and re-stain the entire floor. It would be more costly to go this method and the beveled area would still not look correct. 

He quoted $746 labor to fix the area, and I am looking into getting quotes for the materials. I am expecting around $650 in materials due to the high quality would previously used.

Who is responsible for this? The sellers or the movers? Do the sellers pay up and they go after the movers? What do I need to do besides get quotes and send to my agent for review? What should I look out for to ensure this is done correctly and paid for? Looking for any advice and recommendations.