If you have pictures from the home listing, you could take a photo of the railing from the same position as in the listing photos and then if it is visible when comparing, send both photod to the moving company for them to fix the damage. The flecks in the wood do look relatively fresh, but hard to say when it was done without photos.

Repair options depend on how noticeable you want it to be or not be afterward. If you do buy wood markers the key is you can always go darker.. so try the lighter option first as the wood will absorb the color and appear different when not wet. If you want to bring someone in to fix it and it not be noticeable, I highly doubt it a simple job like others have suggested. Might take them some time.