Just because you don't have a frequent flyer account with JetBlue doesn't mean you don't have travel bank. It can be searched by your name, email, or phone number. If you purchased directly through JetBlue, it should be easy to check on the existence of a travel bank. If you booked through a third party, your best bet is to have your confirmation code that will have a profile number that can be searched, or ask to search by name. I wouldn't even bring up the rest with the agent - just say you are looking for a travel bank that you think may have been issued.

Also, JetBlue has no way to refund you other than the original credit card used. You cannot request a check or return to another card - it's a flag for fraud. Your bank needs to handle this.