First of all, delete all the private or secret conversations at once then follow the following steps:
1. Open Messenger app.
2. Head over to your profile by clicking on profile picture at the top left corner of the screen.
3. Scroll down to click on the secret conversation option that comes with the white lock icon.
4. Finally, click on the delete all the secrete conversations option.
It is pertinent to know that this process won’t delete messages on your friend’s device.