Thanks for your patience. We’re putting Hiding the “Conversation History” folder (and other empty, unused folders) under consideration, for possible Outlook.com improvements.Amkaya commented
I support Anonymous. Stop this clutter and conversation history folders. Get rid of them or give us the option to remove/delete them if we don't want them. ALSO, in the Outlook app on my iPhone I went to Help & Feedback > Contact Support. I sent a message and got a reply. NOW, how can I delete this conversation since I don't want it to sit there forever???? Or will it auto deleted after e.g. 30 days???