Clearing your thread history with a particular contact or group deletes all of your past conversations and call logs from the Light Phone II device. This is a permanent action that cannot be undone. Clearing the history does not block the contact from future communication, it only deletes the history itself by removing their name/number from your recents list. Clearing does not delete the contact itself from the phone.
How to clear your history with a contact/group:
Open the thread with the contact or group, either from your recent history list or by searching for the contact. Click the name/number of the contact at the top of the thread to open up the "Edit Contact" page. At the top left of this page, you will see the option to CLEAR the history. You must confirm the action as it cannot be undone once erased. After clearing the history, you are returned to your main recents list once again.