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 commentJoyce Skeldon commented
I would also like the option to delete complete conversations. My list of recent user keeps growing and growing. I will most likely not be contacting these people again. I rather be able to keep a short list of recent users,I contact frequently.