I take it that you paid for an e-ticket for your parents. I would err on the side of caution, and do the following. Xerox your credit card. Handwrite a note on it that your parents are authorized to use it for the tickets that you have charged. Sign it, and give a contact number for you that will be valid on the day they travel.

It is unlikely that they will be asked for this documentation. But should they be, they will be able to produce it.