BD need to get their act together. The system must know your card is GB issued and charges the fee accordingly, but it's just not on. It's hardly strange to be booking LHR-TXL on that website, but besides that it's unacceptable to charge the fee when it says 'Gebührenfrei'.
Moreover and not necessarily relating to your booking considering bmi MC & Amex are not issued in Germany by BD its ridiculous to be charged a fee for those specific, GB issued cards when they are clearly 'Gebührenfrei'.