To be safe when flying international w/o the card, try one or more of:
. Keep the expired card
. Get a copy of a card if it was not yours
. Plan for an extra 30 minutes
. Go to a physical ticket desk in advance
. Use a third party agency to buy through
It is not the end of the world if you can not provide the card, but can delay you.
I have been tagged once (BR, not DL) and it was 15 minutes of phone tag with Amex, but the airline would have run the exact same charge through another card if need be.
There have been some reports on other airlines of pax having to pay full walk-up. Do not know how real that is.