Calling and asking for information

This place had called me and I had started giving them my credit card information.  They wanted all my credit card service.  They stated that they had all this information, but could not give me the information.  I had gotten rid of them, called my credit card and had my credit card reissued.  My credit card place stated that they would never call me.  If they wanted to contact me to lower my interest rate, must be in writing to the credit card place.  They would review and all information would be done by mail.  This Card Member Services has since called my 2 more times to get my information and state that they are legitimate.