On the SMS & Voicemail Notifications page, you can choose to Hide, Mark as Read, or Mark as Unread. Using the Hide options, removes the notification from the notifications view and cleans up the page, but all communications remain in the Communications area of the actual lead record.
The intention of the Hide option is to clean up the notifications page to make working the leads and ongoing communications easier, but, without "deleting" those communications from the lead record itself. The only option to "delete" communications is to delete the entire lead record.
