Attacking an embassy is war. That is effectively what it is. By definition, an embassy is land held by another state.
So that land, is owned by the United States of America. Attacking it, is an attack on the US.
If it were me.... and thank G-d it isn't..... I would have a sign in front of the Embassy saying the protest was heard, but if they cross the line onto US soil again, their lives are forfeit. And I would have snipers on the roof, and the next guy that storms the gate would get a bullet between the eyes.
Fair warning, and 'pop' gone.
That sounds emotionally satisfying, but before deciding how to respond, it would be a good idea to remember why we are there and what we are trying to accomplish and how this or that response would effect the success of the mission.
The worst thing you can do, is show weakness. It doesn't matter what the mission is, if they don't respect you.
If the mission doesn't matter, why be there at all? Force protection is necessary, but if we create too many dead bodies it will be counter productive and the mission fails.
IF THEY DO NOT RESPECT YOU.
If they respect you, you can engage in the mission. If they don't respect you, it doesn't matter what your mission is.
We don't need their respect, we just need to protect our personnel and property, and we are doing a good job of it. Just to be safe, 100 marines have been brought in already, 750 are on the way and as many as 4,000 more may be moved there. With loads of fixed and rotary aircraft just minutes away, the US already has sufficient power to repel any further attacks, but if we kill too many Iraqis, the mission will have failed.
Iran is crafty. They sent Iraqi militia that are loyal to Iran to attack us, so when we struck back, we killed Iraqis, not Iranians and now the Iraqis are furious at us and the Iraqi government has to try to distance itself from us. Part of the mission is to maintain Iraqi sovereignty to contain ISIS and Iran, but if we kill too many Iraqis in the process, the mission will have failed. In effect, Iran has been using our superior military power against us. To put it another way, the more these Iraqi militia respect and fear our power, the greater Iran's influence in Iraq becomes.