Originally Posted by
chickenmittens
... tried to transfer the points from our Amex account to Emirates but it wasn't working. Something to do with recently switching Amex cards (both cards were in the same account and the points are still in there).
This is a known limitation of Membership Rewards transfers to Emirates, see reports here:
MR to Emirates after changing MR account number
No doubt it is accurate that American Express does not have a
policy for handling transfer failures this way, but they need to listen to the recording of your telephone call and decide to honor the offer or not. However, I don't think a "dispute" is the correct way to handle this, because you did authorize Emirates to charge your card. Your disagreement is with American Express, not the airline. I would pay the bill and pursue the claim separately.