There is no "their people" there hasn't been any kind of election since 2006 where Hamas won minority control of Gaza. A year later they cemented control by arresting, killing or expelling opposition politicians. Hamas has always been a militant group not a political party.
The leadership of Hamas doesn't live in Gaza and doesn't care about civilians. As for the Israeli government, Netanyahu seems to prefer hardliners in control as this lets him have an excuse to take a much more hard line approach to use of force in Gaza.
There is no one looking out for or caring about the Palestinian people.
Palestinians are specialists in terror, if Hamas truly didn't represent the will of the Palestinian people I think they'd be able to make much more progress against them than against Israel.
Actually they want the Palestinians gone and land control, so if Hamas surrenders, it wouldn't bring back Gaza or even change the situation much at this point.
They spent this entire time taking land in the west bank despite it having nothing to do with Gaza nor even geographically connected. So that right there sums up their goals.
Israel is the dominating military force, if they wanted to, they could have easily dismantled Hamas years ago, especially considering they are the ones who supported its creation.