The airline reached a new credit-card agreement with Barclays Plc and MasterCard Inc., said one of the people, who asked not to be identified because the deal hasn’t been announced. New York-based AmEx, the largest credit-card issuer by purchases, has partnered with JetBlue since 2005. Airline deals are prized by credit-card issuers because they often come with annual fees and the promise of awards for free trips can lure customers to spend more.