Is your "line of credit" with Orbitz, DL, or KLM? If Orbitz, then you must rebook through them and follow their rules, which can be stricter and more cumbersome than an airline would impose. However, if a phone rep says something that seems strange, wrong, or questionable, hang up politely and call back. Escalate to a supervisor if needed. You also need to ask whether a KLM marketed (codeshare) but DL operated flight would work, although it might be hard to book such flights on a purely domestic itinerary. Do you understand the expiration rules for your credit? If you can find the T&C, reading them might be very useful.