Yes — you can move or cancel any booking yourself. You do not need to send the invitee a link and wait for them to do it.
Where the buttons are
Open Bookings in your dashboard.
Click the booking you want to change. This opens its detail page — the buttons are not on the list view, which is why they can be hard to find.
Use Reschedule or Cancel on that page.
What each one does
Reschedule lets you choose a new time and moves the booking. The invitee is notified of the new time and the calendar event is updated in place, so nobody has to re-add anything.
Cancel cancels the booking, notifies the invitee, and frees the slot so someone else can take it.
When to use this
The most common case is an invitee replying to their confirmation email to ask for a different time. Because booking emails come from you with your address in Reply-To, that reply lands in your inbox — so you can simply open the booking and move it, rather than sending them back to a booking page.
It is also the right tool when a date shifts for reasons the invitee did not cause: a venue change, a rescheduled shoot, or an interview series moving as a block.
What the invitee can do themselves
Invitees can reschedule and cancel from the links in their own confirmation email. If you would rather they handled it, forward them that email instead — see Rescheduling Your Booking and Cancelling Your Booking in the For Invitees section.