I think the OP meant that Israel doesn't officially recognize Hamas rule over Gaza (because Hamas is a terrorist organization, and it also doesn't recognize Israel). But Hamas de facto rules over Gaza, and as a result they have (slightly) moderated their behavior.
It's true that Israel does not consider Gaza to be Israeli territory, nor does it want to annex Gaza. And it hasn't actually occupied Gaza since Ariel Sharon as PM ordered the IDF to unilaterally withdraw, although Israel and Egypt do maintain a shared blockade of Gaza.
I think we should note though that the Egyptian blockade of Gaza seems far stricter than the Israeli one (which just seems to control that weapons and things that can easily be used to create weaponry or tunnels aren't brought in).
> things that can easily be used to create weaponry
Just to be clear, this means items like food, paper and any and all electronics.
Israel maintains a strict calorie limitation on Gaza, because Hamas turns any excess into rockets. Of course, this doesn't actually deter Hamas that much, because they care about shooting at Israel more than they care about the health of the population, and so a huge portion of the population of Gaza is chronically malnourished.
> Just to be clear, this means items like food, paper and any and all electronics.
You'll find that if you look behind Hamas approved sources (not Israeli propaganda, but local sources in Gaza) you might get a mlre nuanced view.
> and so a huge portion of the population of Gaza is chronically malnourished.
The problem in Gaza does not seem to be the supply of food but the distribution. Hamas is notoriously corrupt and evil as written about in length by their own. To them I guess it is even beneficial if their people us malnourished when journalists and UN officials arrive.
Besides: Hamas needs only to start behave civilized, start imprisoning the violent ones instead of sending grants to martyrs and you will probably find Israelis a lot more cooperative vs now when they openly say they want to destroy Israel.
Israel recognizes Gaza (as something else than Israel at least.)
It is mostly journalists (and internet forums) that conflates Gaza with an open air prison.