Even you can use some header to add the Ticket ID.

In our case we need to remove the Ticket ID: xxx from the subject ONLY when the ticket is created from "Support" -> "Open New Ticket" menu.

If user reply it's OK for us to generate a new ticket from that customer's email and see the Ticket ID in that thread, but NOT when our staff creates it from "Support" -> "Open New Ticket"

Thanks in advance.