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 commentLynda Shirk Williams commented
I would like the option of deleting the conversations. Having all of the old chats listed sometimes makes it hard to find the new ones. I have missed messages from my supervisor because of all the clutter.