Ticket Closing Rule controls this. You need to clone it, as Ticket Closing Rule Restaurant, remove the Execute Kitchen Orders Print Job action, and change the mapping to Restaurant Department.
Then go to the original Ticket Closing Rule and change the mapping to Delivery.
I have tried this…
However, Ticket closing Rule for the Restaurant does NOT work. Status for the table does NOT get updated. please see attached screen capture of the issue.
Your problem is bigger than this.
You have no Ticket Status, or Order Status in one of those examples.
Did you clone the Ticket Closing Rule or create a new Rule?
Can you post the settings in the Actions for the Rules too please. Something is missing.