Often companies you are associated with will share your information with "carefully selected organisations" so they can tell you about "offers which may interest you". It could be one of these. They cannot use your credit card without specific authorisation, so the fact they didn't ask for details means they cannot legally use it (not that they can't use it).
However some words of caution - I hope you didn't give them your address or postcode. Never give that infomation to people who call you, or more importantly, more confidential information. I have "had words" with companies who call and then start asking for my date of birth or mother's maiden name. They are told where to go. BTW This is why many companies now ask for selected bits of information eg the 3rd and 5th character in your password.
If you are unhappy (and it sounds like you are) call Barclaycard and check them out. Then I would recommend telling Barclaycard that you want them to take your name off the list of people who can be contacted like this - they are obliged to do this. Good luck. And as general advice - never buy anything from someone who calls you.