“But Gaza belongs to Israel.”
True, but it might be more trouble than it is worth. Since Israel pulled out and gave them autonomy, they make no money on Gaza, but still incur lots of costs. The population is a demographic bomb, that Israel does not want to incorporate and grant voting rights. It is a den of terrorist vipers, and Egypt can go third world on them, whereas Israel is restrained in the tactics that they can use.
The question is whether Egypt can be trusted long term, or if an islamist regime might be back in the future.
I don’t think that Israel should “take it back” unless and until all the Palestinians are removed from the territory or killed. And I really don’t care by which means they are “removed.” As far as I am concerned, their dead bodies would make good fertilizer for the land after “the dust settles!”