Hi Roy,
Outlook doesn't provide a build-in option to automatically clean up conversations. If you want to do it automatically, you will need to find some third-party add-in or you can try posting to the Outlook for Developers forum and see whether this is possible
via codes:
https://social.msdn.microsoft.com/Forums/office/en-US/home?forum=outlookdev
The reason why we recommend posting appropriately is you will get the most qualified pool of respondents, and other partners who read the forums regularly can either share their knowledge or learn from your interaction with us. Thank you for your understanding.
Regards,
Steve Fan
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