Moving an appointment cost a phone call, and if your customer did not pick up it cost two.
What is new
On an appointment you can now propose a new time. You pick one or more times that suit you, your customer gets them by email, and whoever clicks one has moved the appointment by doing so.
The proposed times are reserved for that one customer until then. So nobody else can slip in and book a time you have already offered, which is exactly the scenario that otherwise leaves you phoning after all.
If you see a faint amber band while dragging an appointment, that is a time currently offered to a customer. From the message you can withdraw that offer if you need those minutes after all.
If your customer does not respond
The offer has a running time. When that expires, the minutes come free again by themselves and the original appointment is still simply there. There is nothing for you to undo.