How do RSVP invitations work in getregistered?

You can configure invitation declines in event settings. When enabled for an event, any invitations you create and send out will include a link the attendee can click, as usual.

When following the invite link, the invitee will see a screen prompting them to accept or decline the invitation. From this screen they can provide a reason if they decline:

Invitees who have declined an invitation can refollow the link later, to revisit their decision:

Within your admin area, you can view the Invitation status - and decline reason - from the Invitations area: