Hi,
You can create a retention policy in Exchange that will remove old messages from Conversation History folder. Note that if you run Exchange online this process only runs once per week so even if creating a retention tag that deletes after one day messages
can stay until Managed Folder Assistans runs (or create a script to run every day).
https://support.microsoft.com/en-in/help/4013794/how-to-clear-conversation-history-by-using-a-retention-policy-for-an-e
