I believe as per the Oslo accords, Gaza is supposed to be part of the Palestinian Authority. The recognized PA does not control Gaza, so I believe it is de jure a Palestinian territory in rebellion.
It's even messier. As part of the settlement leading up to the elections, that Hamas won in Gaza, Hamas made a lot of tidying up of its profile, including all manner of declarations of policy in accordance with the principles of democracy etc – all designed to make Hamas sufficiently palatable, "normalized" etc. to get to run in these elections. And of course it then turned out Hamas was just be engaged in some very opportunistic lying.
So it's not a simple matter of Gaza supposedly rightly being under jursidiction of the PA, since the PA is only one possible expression of the Palestinian democracy that was supposed to be the outcome of a process (that is now pretty much stillborn, and the PA is not very democratic either, never mind how bonkers Hamas is). Hamas is a grass-roots organisation, numerous and popular enough that it simply could not be sidelined and completely shut-out of the election process back in the day. Doing so would have de-legimtimized the elections with large parts of the Palestinian public before they even happened. Especially since Hamas was playing nice, and making all the right noises and moves at the time.
(There were obviously misgivings about their sincerity, but only hindsight is 20/20, and it is possible at least part of the Hamas leadership thought there would now be a Palestinian state, peace and democracy, and so Hamas needed to actually change in accordance. There was internal conflict over it. So everyone with misgivings sort of still had to hope the crazies would not win that one, and maybe things could have come right in the end. And then it all went to crap.)
Besides, while the PA (PLO, Fatah, but not Hamas) has recognized Israel, it is not at all as clear that Israel has recognized the right of any kind of Palestinian state. According to that line of reasoning, all Israel has so far done is recognize the PA as a legitimate representative of the Palestinian side, someone it might actually talk to. (Which is a kind of progress, if the alternative might be denial the Palestinians even exist.)