I would assume, maybe wrong, that any property owner has the right to remove the limbs from any tree extending over his property.
The tree owner may object to climbing his tree for you to do so however.
A well placed ladder might avoid this problem however.
Just be careful, I recently smashed my thumb when the rope used to pull the extension up on
my ladder broke and the extension came down so fast I couldn't move fast enough, or even think
fast enough to avoid it. Sure did hurt and I was lucky as, I suppose, my thumb could have been
slice off. I got lucky.