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 commentJanet commented
I would like to see the option to delete old chat conversations. If the subject has been dealt with, why do I need to keep the old stream? It just creates clutter, as mentioned by another user