I second its a against the law to install them in many state and federal lands,
there are rules against it
on private lands, I also agree if NOT your lands, ask land owners first, better safe than sorry and loose a good spot due to something so small!
as for leaving them in as to taking them out
I will say IMO< leaving them in is better, as your ONLY damaging the tree once and MOST tree's will grow around it like said above, most tree's encounter damages along there lives and most will survive a metal object installed in them, but some are more sensitive than others
I have tree;'s that have had box hooks screwed into them for 20+ yrs and no issue's minus the hooks them self getting damages as the tree has grown over most of it!
IF you screw it in and remove it and repeat, your causing stress to the tree every time you do so!
installing ONCE and leaving it, also the tree IMO< to tolerate it and grow around it!
they do sell strap on hook/holders too if you rather into have to worry about things at all!