It's not 100% clear by this article what was said, and I don't have access to the source article either. But I think the parts, even if they don't mention verbatim what happened, makes it a pretty clear threat:

> America, Colby and his colleagues told the cardinal, has the military power to do whatever it wants in the world. The Catholic Church had better take its side.

> As tempers rose, an unidentified U.S. official reached for a fourteenth-century weapon and invoked the Avignon Papacy, the period when the French Crown used military force to bend the bishop of Rome to its will.

I'm also not 100% sure what they mean with "invoked the Avignon Papacy", a bit like saying "Invoked the Second World War", it was an event/time period as far as I know, not something you "invoke" exactly. But even mentioning it makes it pretty clear what they're hinting at to be honest.