Typically when buying American Express, Mastercard or VISA gift cards you pay above face value, and this negates the point or mileage benefits. Look at the package for a disclosure of the fee.
I noticed a $3.95 fee when purchasing through Amex. I'll need to check again at the grocery store, but they seemed to be at face value. Interestingly, Amex no longer ships gift cards to a number of states (including CT), yet they sold locally.