Directory comes with a feature where you can choose which mode of communication is preferred by the clients and then you can opt-out of all other modes by just a click.
The icons highlighted in orange denotes preferred mode whereas as the blue icons denote opted out mode of communication.
You can find similar information on communication preference at Account level under contacts.
If the header “Do Not Contact” does not show up in the contacts section then you may have to add that to the column by selecting it from the “Select Table Column“