To edit the invitation simply click Edit on the invitation in your home page. You will see the availability you provided and will be able to add or remove availability. You can make any other desired changes and save. This activity changes the invitation but does not change its invitee link. So all you have to do now is ask your invitees to visit the link again and provide their availability.
Note that if you make changes to the availability you provided and some invitees have already replied, their replies may be erased. For this reason you should tell them to review their availability again. ScheduleOnce will recognize them and allow them to edit their availability.