For the itinerary that you want to truly DELETE:
Go to the itinerary title box (on the AXUS side).
Click the Gear Icon to EDIT ITINERARY.
Click the box "Stop ClientBase import" at the top of the pop up window.
Go to the 3 dots on the far right past the dates
Choose DELETE ITINERARY in the dropdown menu
If you don't check the box and then delete the itinerary, a new itinerary will sync over.