Note: Most travel agencies (usually in North America) when selling non-discounted full fare C fares will use the airline's merchant account to charge your credit card instead of their own merchant account. To the credit card company, it would look like a charge is coming from the airline itself and not the travel agency.

I have a credit card that gives me extra points for airline bookings as well. However, I always book them through a travel agency and tell them to input my credit card number directly into GDS when issuing the ticket as opposed to running my credit card through the travel agency's own credit card merchan account. This way the merchant shows up as the airline and not the travel agency on my credit card statement and I get the extra points.