There seems to be some confusion around how this works. First off the ability to delete messages is off by default.
The IT Admin who setup the Teams environment will need to turn on the admin ability to delete messages. Once they have enabled the functionality, admins will be able to delete user messages.
If your IT Admin as enabled it and you still are having troubles please let me know in the comments below.
An error occurred while saving the commentPhil Walker commented
I think Warren is referring to the setting in the Microsoft Teams & Skype for Business Admin Center under Messaging policies. Its should be listed as 'Owners can delete sent messages' under all of the profiles. We have it off at the moment so I'm asking for it to be switched on.
You can make these edits using a cmdlet, please see the documentation at https://docs.microsoft.com/en-us/powershell/module/exchange/users-and-groups/Set-UnifiedGroup?view=exchange-ps
This should help you make the edits requested in this topic.
Thank you for your votes and comments on this feature. The team is in the process of finalizing designs for deleting private chat threads. I will update as we have more progress to share.