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 commentAnonymous commented
WTF?! Why cant I delete chatter that was once important to me only, but no now? Huh??? Is Microsoft retaining and reading my chat?