There was a tree where the trunk was entirely on my neighbor's property, but some of its branches were over my roof.

The day before yesterday, an employee of the company (not sure of position) asked for permission to come onto my property to remove branches and clean everything up after finishing with the tree. I voiced concerns that my roof could get damaged, but he reassured me no damage would occur. If it's important, it was pretty broken English, so I am not positive of exactly what he said, but I think that's the jist. He said, "No damage, no damage."

Yesterday, after they removed the tree, I noticed some bent pieces (it's a metal roof). I had a roofer over today who said it's pretty minor, bending in a few places, probably just cosmetic, but one part could possibly leak. He's working on getting me an estimate.

So is the neighbor liable? The company?

And what do I do from here? I'm trying to get the company's name, but that's been a challenge. I saw a name on my security cameras on the back of their shirts, but a Google search is turning up nothing.