If you want to invite participants to reschedule but remove their original time(s), do not use the rescheduling feature. Why, you ask? The reason is that deleting a spot will break any reschedule links sent for that spot.
The reason is that the rescheduling system is tied to the original time, so the rescheduling link will stop working as soon as you cancel.
To be extra clear with your participants, customize the Cancel email to say "We'd like to reschedule and you'll receive another email shortly with a new link to pick times." Additionally, customize the Invite Previous email to say "Thanks for being willing to reschedule. Please pick a new time here."
That way you can delete all the original times without breaking the reschedule links.
When would this come up?
One common rescheduling scenario is that you need to move participants to another week or set of times, while making sure that nobody can still pick times that were originally there. Like say moving everyone from one week to another week. There are three scenarios below that have different ways of handling this:
#1: No Confirmed Participants
If you only have "potential recruits to invite" just delete the spots and then use Invite Previous.
#2: Invited Participants
Cancel the invites per above, and then use invite previous.
#3: Confirmed Participants
Also cancel first, then invite previous