"Response: After a player claims 1 or more power for his or her House, move that power to a character. "

We're having some difficulties in our playgroup determining how much power actually can be gained with this event. Is it cast at the end of the Framework Action following player actions (following the kneeling of defenders), or for one particular step of this framework action?

In other words:

If player A makes a 2 claim unopposed power-challegne against player B, can player B play "Infamous!" to claim 2 or 3 power? (2 for the claim only or 2+1 for claim and unopposed).

In the example you used, I believe the answer is 1. Power gained from the challenge is actually 'moved' from the opponent, not 'claimed'. The power from unopposed, _is_ claimed, so that one you can move to a Lannister char.

This is correct.

You have to identify the separate effect Infamous! is Responding to (in this case, claim or unopposed). You only get the power claimed for the one effect you are Responding to, not for all power claimed for all separate "claim power" effects that have resolved to that point in the action window.

And yes, the "claim" of a power challenge cannot be grabbed with Infamous! because that power is "moved" from one card to another, not "claimed" from the power pool. (This is the same reason a player using the Siege at Winterfell agenda still gets his "prize" for winning a power challenge.)

Thank you both, as always, excellent replies!