Dear Prudence: I'm tired of my friend attributing a successful surgery to God
Where I agree with Prudie:
No, don't let your friend know that you're annoyed by their religious displays. There's a bigger issue at hand right now and you should instead exercise your patience and polite, noncommittal generalities when the god-talk comes up, just as you do when your friends ask if their child's frightening drawing wasn't the most beautiful thing you've ever seen: "yes, honey, that's very nice."
Where I disagree:
...But let's not sing unnecessary praises either. Prudie does NOT know that the newly religious friend dealt with the matter better because they became more religious. Prudie does NOT know that the the medical staff was thanked beyond complimenting them on being such nice tools for J.C. to use; Prudie should understand the difference between that and thanking someone for their hard work. And no, you should not commit the ethical blunders of lying and encouraging behavior you don't endorse as advised by Prudie in the last sentence.
Simply focus on the wholly human medical miracle that took place and gently ignore the prayer-talk without getting into arguments about it. "I knew your daughter would be fine - she's a strong little thing!" instead of "Yeah, well explain why Jesus didn't heal hundreds of millions of other people in the world, HUH?" Not because the latter isn't a valid point, but because you're trying to preserve a friendship.
P.S. To clarify that last paragraph: lying by omission is still lying, but given the limitations of the human condition, all you can hope for is to keep your friends on the best possible terms. This will include either complete avoidance of a topic (omission of your true feelings by selectiveness) or outright falsehood (pretense of agreement with your friend's feelings). Omission is, in my humble opinion, the wiser option.