If the claim was correct, ie you DID use a non-royalty free recording of the piece of music, then you cannot do anything short of removing the video and re-uploading it with royalty-free/creative commons audio (I very much like Kevin's work too:  www.incompetech.com) so that you won't run into the claim situation (with as much certainty- there are never any guarantees that it wont be misindentified).

Meaning- you cannot claim that the copyright claimant has no claim.  Because you certainly do not and therefore the claimant may well have.