"但属于我家的。" do they know

no expert here, just my thought.. the damage is done and you do not want to have a bad feud over this with your neighbor. but you should have told them the tree belongs to you and only you (or maybe the city) can do anything, and they should have asked for your permission. convey this in a polite but firm tone so that next time they will take a second before doing something else between you two. or you may ask them to plant a new tree there, so they do get a civic lesson. in the end, you need to tell your displeasure about this and try to maintain a relationship.