You realise Hezbollah originally 'annexed' part of Southern Lebanon themselves after they were expelled from Jordan? Then proceeded to start firing missiles at northern Israel, amassing arms (guess where they got those from!) and digging a huge tunnel system. They've pretty much pushed out the original civilians from there so that they can spend their days plotting how to attack Israel. The Lebanese government needs to deal with all this, but they haven't and won't, because they've also been infiltrated by Hezbollah and are actually stronger militarily than the Lebanese army! Gaza was worse because Hamas became the government. If the people were to try to get rid of them, it won't end well and thousands would die, just like in Iran. It's a tragedy.
Like a cancer that spreads through a region you can try to remove these terrorists but they always come back. This is why the US won't be able to get rid of the IRGC in Iran, nor Israel expel Hezbollah from Lebanon, because these groups are set up in a way so they regenerate, even if a 'military giant' tries to wipe them out. That's their strength. Even if you killed every living person in Lebanon you wouldn't have wiped out the ideology, nor people elsewhere who will one day return and start all over again.
All this killing is abhorrent, but I will by no means say Israel is somehow 'worse' than these truly awful terrorist groups (which seems to be the majority view on this forum), who hold entire populations hostage with their threats and teach young children hatred, because if these groups have their way, they will destroy Israel and kill all Jews (they've said that's their goal!). Don't think they won't come for us Western infidels next. So what should Israel do? No easy solution to be found. What do you think they should do?