You are there to get your money and nothing else. Right? They do not need your total rewards number cash you out. The TITO system verifies the tickets as legitimate (that's why they scan them as they total the amounts up).
You cashed out over 5,000 worth of tickets, perhaps this generates and automatic report to the IRS, as when banks deal with at $5,000 plus cash transaction. Barring that, who knows, but I would not comply and just say I don't know it or I don't have a card. Let them take the next step.
It doesn't make you any more money, so why bother complying with this at all?