Call center recording my credit card info


I just made a new contract over the phone with my mobile phone provider and I needed to pay the activation fee. The lady told me that they could accept only credit cards and asked me for the full details (number, expiry date, and security code, the usual stuff) over the phone.

However, she took the details personally (to input them in whatever database they use) and the calls are recorded.

I am now concerned about the security of my information: not only she has full access to my credit card, but also whoever listens to the recording. It’s a big and well-known provider, so I don’t think they could do something shady, but it still bothers me. Is it really acceptable? Should I have refused?

(Note: I live in Switzerland and I don’t know exactly what are the data protection regulations here)