Removing the Conversation Tab is being reviewed by the feature team.
For deleting chat messages, please following progress here: https://microsoftteams.uservoice.com/forums/555103/suggestions/33535006.
An error occurred while saving the commentDenise commented
I would like a way to delete or clear my recent chat history. I don't need to have a running list of all of the chats I've ever had. It just clogs up my Teams application. I know I can hide individual chats, but that's tedious. It would be nice to have a option to "clear all chat history".