WHAT, wait, OK. So somehow they've convinced you that this was an actual medically necessary procedure. I disagree, but I'll put that aside for now. They still performed a non emergency procedure on your child without your consent.

I highly recommend you have your daughter evaluated by a doctor from another city (and I hesitate to say another culture... but that's the choice I would personally make). They need not even know your relation to the "famous" grandfather. If they ask, just say your not related. Use your maiden name if you have to.

But lets talk about consent for a moment. Doctors need consent to operate on someone. In emergency situations it's implied, but as far as you mention your daughter is healthy. So that means it's your job to decide on behalf of your daughter. She is unable to communicate consent, so she cannot consent so you have that power as a parent. Because that's how you don't end up in situations where mysterious surgeries are performed and you have uncertainty about the reason.

You would not want this to happen to your own body. Wake up one day and someone gave me non emergency sugary because "it needed to be done". Fuck no, I'd not allow that to happen to my own body, and nether would you. So your daughter gets the same rights. Regardless of if it was necessary or not, they need to get your permission as long as you are conscious to give it.

He's a doctor, he understands parental consent. Therefore he should have been more aware about notifying one of you and getting permission. Also, did he operate on his own family member? That's generally not permitted in any modern medical establishment particularly without locked in parental consent.

So don't be scared of him. He should be scared of you, also don't worry about the money aspect, because if you go full nuclear you can VERY likely get medical malpractice money. Shit, given the family relation and dubious consent, a loss of a lawsuit might put his licence in jeopardy. Certifiably if he's as medical celebrity as you claim, the media might be interested in such a situation. That would be unfortunate for both of you, but you would come out smelling like roses... he may not.

Perhaps, this can be resolved without taking it that far, that would be nice. But this is a time where you need to enforce your authority, on behalf of your child, and do not make the mistake of thinking you don't have power in this situation.