We purchased a single-family home in Springfield, MA in 2011 that we are using as rental property. An abutting neighbor demands we remove a tree branch (tree is in our yard) that hangs over her yard and has damaged her fence as it has grown. An arborist estimates tree is 15+ years old. We gave neighbor permission to remove branch herself, but she says it is our responsibility. We said we'd work with her, going as far as hiring a company to remove the branch, but she is being quite demanding and won't release us for existing damage (which most likely occurred several years before we purchased property). Legally, do we have to remove it and pay for existing damages to her fence?