How could they charge me a fee if they don't have my credit card information?

should complaint to CRTC.ca.

Ya. Just called but we were not at home. No message left. Gone to the filtered list.

be careful if you pressed any key according to what they told you, you may start paying fee.

Automated call regarding interest rates. Press 1 if you're interested.  Press 9 to be removed from their system.  We'll see if we are really removed from the system.