From the HUB:
If you don't want to see all of the read messages and conversations in your history, we would recommend filtering the inbox by "unread" messages. If you still want to delete the messages, scroll down for directions on how to do that.
You cannot delete an entire thread or conversation history. Each text has to be deleted individually for each person.
To filter by "Unread" messages:
1. In the HUB, go to your inbox tab, click "filter", and then select "unread"
To delete a single message from a conversation:
1. Click the person's name in the inbox to open the conversation box
2. Click the message box you want to delete. This shows the details of this message along with different options you can select.
3. Click "Delete" under the message
4. A box will pop up to ask if you really want to delete this message. Click "delete" to continue and permanently delete the message from the history.
5. The message will not be deleted and you will see that it's been deleted in this conversation history.
From the Inbox 1.0:
You no longer have access to the Inbox 1.0