Will a screw or nail in a tree kill it?
Does a Nail or Screw in a Tree Kill the Tree?
My opinion is that nails or screws can introduce illness into the tree. Generally speaking bark is a tree's skin and should not be opened. Last year I successfully hung a birdhouse on a tree with bungee cords. So if you are wanting to hang something try to experiment with ways that won't puncture the bark.