Call again. Soon. Someone else may know how to do this. After 24 hours, you may have to pay for a new ticket and pay the penalty for cancellation as well as any rate changes. It's not really likely they will let your grandmother board with two completely different last names show on passport and ticket, and they will not allow boarding merely with a CDL - it's not sufficient to allow entry into Mexico. Not likely at all.

(It may be they were saying you would get the difference between the cancellation fee and cancelled ticket as a voucher?)

Unless... maybe... she has a marriage certificate or equivalent, legal with notarization or stamp, that shows her name was Briones and is now Garcia. And I'd still check with the airline (and I'd maybe still not trust them, as if they let someone board who may be refused entry into Mexico, they can be fined significantly - most employees are very aware and do not want to be the one responsible for costing their airline a lot of money and a free flight back).