Here's
FinCEN 2010 - G004, FinCEN's most recent and most detailed guidance on the travel rule. It focuses on what you are required to send; i.e. if you adhered to its requirements as the originating bank you have complied and later breakdowns are not yours to remedy.
If you sent the required information, any intermediary bank is required to forward it so the beneficiary bank should ultimately receive it. (
Note the explanation in the Guidance that indicates the intermediary bank is not obligated to send everything you might have sent, only the information required by law.) From my perspective, if you are assured that the information you sent never actually made it to the beneficiary bank you could freely provide it to them in response to a follow up request.
However, if the beneficiary bank wants additional information not addressed by the travel rule, but perhaps by their policies or even the laws in their country, I see no basis for providing that after they have accepted the wire unless there is some international or systemic authority for doing so. If they are refusing acceptance because they want information beyond that required by U.S. law, then I'd let the customer decide what we would and would not give them.
Others here have more first hand experience with international wires than I do so give them a chance to respond...