I'm not sure why you weren't told at booking that the card would be required, but it is stated on the website that the card may have to be shown at check-in. The best advise I could give you or anyone traveling internationally is always carry the card with you or if someone else is purchasing the ticket please have them go to the nearest airport/ticket office to have the card verified. Without verification many airlines computer systems will NOT allow the agent to check you in. Also with the high rate of fraud happening its a hassle but it is the best way to keep people from using fake card numbers to travel, and trust me it does happen almost daily that a person is caught for fraudulent card use. I'm not sure if delta will reimburse you for your expenses since you weren't told over the phone, but here is what it says on their website:
Credit Card Presentation
To safeguard against credit card fraud, the purchaser may have to show us the credit card along with a valid photo ID. The time varies based on the billing address of the credit card or the country of travel. If the purchaser is not traveling, they can show us their credit card and ID at an airport ticket counter or another
ticket office location, whichever is most convenient.
http://www.delta.com/planning_reserv...ions/index.jsp