- From the mobile version of the site you can't permanently delete messages at this time.

To delete a discussion that will remain archived, go to the message section and click on the three dots at the top right to delete the discussion.

- Since the computer version you can delete permanently the messages one by one, for that click on the heading "Messages", once in your mailbox:

You can delete a discussion by clicking on the "cross" (the conversation will remain archived)

Or permanently delete a message by hovering over the messages then clicking on the "cross" icon

Web version : 

Mobile version :