For accounts reputation management purposes you can not delete any notifications that have been successfully sent. 

Pushletters may only be deleted if they are in a 'Draft' or 'Scheduled' mode, which is when they haven't been delivered to subscribers yet.

You may delete a Campaign at any time by clicking the big 'Delete' button on the top right of the 'Campaign Detail' page, or by clicking the 'gear' icon > Delete Campaign on your 'Campaigns' page.