Did you redeem the gift card to have a credit balance on your account prior to attempting to make this purchase?
If you did, is the credit large enough to cover the purchase and any sales tax?
Otherwise, the system asks you to verify a payment method when it isn't convinced that the owner of the account is who is attempting to use the account.
ASC - Late 2012 Mac mini, macOS 10.15.2; Watch, series 5 GPS/cellular, watchOS 6.1.1; iPad Air 2, ipadOS 13.3; iPhone 8+, iOS 13.3; TV 4th Gen, tvOS 13.3; HomePods, audioOS 13.3 and Airport Express w/ Airplay 2