If you would like to permanently delete a conversation and its history, you can click on the options menu for a conversation and select Delete conversation. This action can be taken from either active, archived or blocked conversation.This action is permanent and you will not be able to restore these messages. These messages will also be deleted on the site and will not be accessible by your customer.  You and your customer will still be able to message and start a new conversation, without the history from the previous conversation(s).