Keep in mind that Babur also blames the elves for arming the natives and inciting rebellion. He feels compelled to get them out, and soon.
And that's another issue.
He literally has no proof and given the fairly unique equipment elves use it's fairly easy to determine if somebody is using their weapons.
That and he misses the plain obvious fact that bombings were also rampant on the elven side, and these killed even more people. As the first IC post shows the explosions were plain heard from even the other side of the border.
I don't buy this. Babur has number of ways to know Yllendthyr has no hand in the bombings.
At best he may spread this rumor as Babur's casus belli.
Which is actually not a bad idea, either. Branding the enemy as somebody who supports indiscriminate murder against Tinties is quite a good excuse. It works well even in our world.
EDIT: That's the same deal for practically every colonist around that time. They ignore the natives and claim right as the only dominant European power. IIRC, the Portogese also tricked Spain because unlike them they didn't know Brazil is that big.
In your case Babur's response is full of sour grapes. We are well past the colonization so he's asking the impossible by demanding to hand over a well-established state. Please tell me he isn't serious with this and only attempting to goad Yllendthyr into a war.