I think the only thing they really care about is the American hostages. Anything and everything else is just politics and diplomacy that they'll get around to if it becomes a PR issue. PR wise, the US is already claiming it has stepped in to get Israel to step it down some of its measures, but they aren't going to step back when it involves outside parties like Iran playing proxy war in Israel through Hamas, even if it does screw Palestinians who have little say either way.