They probably aren't going to be given much of a choice.
China, Israel, Russia, along side various Middle East and African countries would realistically all demand he be taken out out of fear that he will do the same to them.
And this would be done because he has now shown that at any time he could arbitrarily decide a country's government is evil attack them.
Bullshit.
The world stood by and watched as Queen Beena ruled her nation by liberal application of mind control superpowers.
As in, so liberal that mind control precautions were a routine check for a lot of diplomats assigned to the region.
They did nothing official either when she attempted Grand Theft Qurac; that was stopped by superpower intervention in both Paragon and Renegade timelines.
The idea that superpower intervention in a minor conflict in Northeastern Africa will trigger any sort of censure is not supported by the known facts.
Not to mention that anyone with access to intelligence files has been well aware that any of the Green Lanterns could topple any government they so choose at the will of their bosses.
It's not exactly a new development.
It's one thing to dislike Grayven, but it shouldn't affect your actual critical thinking skills.
Now, the ethical issues behind having a tween and multiple teens do the actual work are a whole different issue.
THAT is where IMO Grayven fucked up.
Where he could do with someone like Renegade Zatanna or M'gann to slap him upside the head everytime he drifts too far into his Hard Man doing Hard Things while Hard mode of thinking.
For example, he just had Lynn do the same thing to those people that she did to her parents.
And it didn't occur to him that there might be bad associations there for his daughter.
And the idea that arming the civilians makes things better is just stupid; give it a couple weeks before they start fighting each other or raiding for food and cattle.
Nor was there any forward planning for intervention forces to keep the peace.
Entirely too much like what we saw in RL Iraq when the Americans went in; no real plan for managing the peace.