Exchange Hybrid / Office 365: Cannot delete shared mailbox

When you try to delete a shared mailbox, which is placed in Office 365 (Exchange Online), and you are running Hyrbid, you may see this:

The following error occurred during validation in agent ‘Windows LiveId Agent’: ‘Unable to perform the save operation. ‘TESTDELT’ is not within a valid server write scope.’

Then when you try to delete it from the ECP on the on-premise Exchange server:
… “isn’t a mailbox user.”

Workaround

Use powershell on the on-premise Exchange:
Remove-remotemailbox –identity testdelt@domain.com

Run AAD Connect delta sync.

You could also delete the user account, for the shared mailbox, and force a AAD Connect delta sync.