Straying off topic a little, but it sounds as if the Danish credit card system is not like we understand it in the UK. The Netherlands is similar in my experience. My bank there issued a Mastercard, but debited the amount on it automatically from my current account every month, with no facility (as far as I could tell) for me to decide whether to pay it all off or not. As such you had to be pretty careful how much you put on your card so you could try and guess how big a hit you were going to get. Upshot was that I generally used the debit card on my account, or even my UK credit card (if I reckoned that the hit on the exchange rate would be less than the hit in interest charges if my NL account went overdrawn).
Back to topic: a tank on the lawn at Waterside might get their attention!