From the Contact search bar, enter the name of the contact you wish to prevent from receiving all marketing materials moving forward (postcards, e-mails, text messages, letters) and select their name to be directed to their contact record.

From the contact's record, select 'Campaign Info' from the relationship tree on the right-hand side to jump to the campaign section of the contact record.

From the 'Campaign Info' section, check the 'Do not market' box in the upper right-hand corner.

Once you've checked the box to disable marketing for this particular contact, any current campaign assignment will be removed, and you will see a noticed that 'Contact is locked out from being assigned to campaigns.'