An email client is, something like.....
Outlook, Live Mail, the new Windows Mail App (in Windows 10) or some other third party software like Thunderbird, Incredimail, Pegasus, etc.
If you are just using a web browser to interface with your Centurylink provider, then you would have to ask them how to control your contacts list.
I remember, not so long ago, Outlook Express had a check box you needed to uncheck or else it would put everyone you replied to into your "address book" / contact list.
It'll probably be something similar you need to check or uncheck, somewhere on the toolbar under options or something similar.