Grouchy old man
ArboristSite Operative
I dunno about this. No contract, a "he said/she said" and nobody was even home when this happened. I would want to hear the tree company's story before deciding this. For all we know the window was damaged all along or it was unavoidable. What I would do is not pay anything to the tree company. Instead, write them a letter stating your position and include a couple of estimates for the window repair. Make them come to you and give their side of the story then the two of you reach an agreement.