I don't recall ever having to show my credit card for a flight checkin.... even when I've bought tickets either directly from the travel agent or online.
May be there have been changes recenty as to they want to verify if the person flying is the same person who swiped the card...dosen't make any sense to me i dont think they should bother as long as it has been paid.

Aana free, jaana free,
Pakde gaye tho khana free.