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 commentJeffrey Hall commented
Being able to delete the entire conversation is a basic requirement. It should have been in place from day 1. All of the other "chat" type applications allow the whole conversation to be deleted. As a minimum, the conversation should be hidden or archived after a period of time. This list keeps growing and I am missing important things in the dross of "I will be a few minutes late" type messages.