I don't recall any kind of interstellar law or signed treaty or whatever that could grant or recognize that right.The Thargoids have a right to claim territory,
("Donkey, you HAVE the right to remain silent. What you lack, is the capacity.")
If they are actually extra-galactic and there is no shortage of space, then laying claim to a territory that's basically our backyard is anything but reasonable.even if we speculate and say they are extra-galactic. Their claims are quite reasonable in size, there is absolutely no shortage of space.
I wonder what would they say about our right to claim a territory close to their homeworld.