I've had this request - it co-incided with the issue of a new credit card, same number, new expiry date. The previous card date was about to expire.
The credit card detail is simply a fall back for them if my nominated bank account has insufficient funds for a payment. I'm a little nervous about this arrangement; the credit card has a very useful limit if it were to be illegally exploited, but there is that risk wherever and whenever it is used.