Man, there's some cruel shitbags on here. Little future Ted Bundys. Chicken and barbed wire. Poison. .50BMG.
I'm guessing you've openly spoken your concerns to them without any innuendo? They get it crystal clear, that you don't want their dog tearing up your tree, and they understand tearing bark off of a tree will kill the tree?
Then try using, before it's too late, liberal coatings of pepper spray. Maybe wrap the tree or treat the wounds first and put that on top? Or only put it on good bark? If you use pitch, you can put the pepper on top of that for sure. The thicker the better. If you empty out a large can in a pot with a bag covering the top to catch overspray, and evaporate off the liquid, you're left with essentially a pepper oil/light grease. It'll stand up to the elements a little better. It probably won't take too many tries before he gives it up.
While I wouldn't hurt the dog, I WOULD threaten the neighbor with that if they just acted like they really didn't give a fuck about your property. I also might tell them that the pepper oil or the pitch or whatever, is some stuff I put on the tree to help nurse the tree back, but that the stuff turns out to be highly poisonous to dogs. Sorry, it was all they had available that would work on that type of tree. So you're warning them to keep the dog away from the tree now for it's own good, please.
While your neighbors, sadly, don't give a shit about you or your property, they likely do about that dog. So while they wouldn't keep the dog away from the tree just out of respect for you, they likely will keep him away from the tree out of fear of losing their dog. Our dogs, in case you aren't a dog lover, are like our kids, our family.
This option has the benefit of applying something that actually might stop the dog if he DOES try it again, as well as motivate the neighbors to watch their dog. It doesn't carry a direct threat or hurt the dog so as to cause tension between you and your neighbor (even worse). The fear comes from "medicine" used to help nurse the tree back to health vs. threatening to poison or kill the dog (or doing it). It may make them better neighbors.
Downside, which isn't all that bad, is if they see the dog lick it, even once, they'll wanna know what's in it to rush to the vet, and you may have to come clean. Even so, it illustrates that you simply wanted to save the tree, not hurt their dog, yet at the same time, spur action from them that assists in both. Again, it may make them better neighbors.
If it makes 'em worse neighbors, well, then you know what kind of trash you're dealing with.
Glad I have good neighbors. Ones that show up armed if the alarm goes off, ones that help out, ones that helped me look for my dog for four hours until 1am on a work night. If you do have bad neighbors and can turn 'em, it's worth it. Good neighbors, to me, are an important part of life. Good luck.
