It's actually quite OK to screw something to a tree or to make a hole (usually done to harvest sap, for example of pine trees or birch trees, which was done for centuries in my country).
It's actually much better than wind metal wire aroud the trunk as I've often seen, because the living part of the tree is a quite thin layer under the bark. Winding wires around can kill the tree whereas digging a small hole, even through the whole trunk, does not. I've even seen some "professional" ways of making cabins in trees that use the technic of placing cables through the trunk.
The traditional way to close a harvest hole is to use a small piece of branch, preferably from the tree itself, roughly carve it until it fits the hole and drive it in with a wooden hammer (or a bigger branch). You can cut the branch close to the trunk, but leave a bit of excess, like 0.5 / 1cm.
It should be enough, but usually it's recommended to coat this with either clay, or natural tree resin (warm it to make it melt, quite simple, but don't burn yourself). Then let the tree heal itself with time.
You can also leave the hook in place as others suggested, but it will heal around it and this will result in a much bigger scar.