Plans change. Either side can move or cancel a booking without negotiating over email.
Their confirmation contains a manage link. Opening it lets them:
They do not need an account, and they do not need to contact you.
Open the booking from your calendar and reschedule or cancel from there. The invitee is notified either way, so nobody is left holding a stale invitation.
Cancelling frees the time immediately — it becomes bookable again for anyone else with your link. Rescheduling frees the old slot and takes the new one.
Ask invitees to keep the confirmation email. It is the fastest route back to the booking, and it saves the "can we move Tuesday?" exchange entirely.
Related: How invitees book time with you · Create a booking link