RSV Calendar Migration Tool - existing links already sent

When using the calendar migration tool, my understanding is that this will update links the tool finds in the RCV users calendar. Does the RCV user then need to update the invite so the recipient will get the updated link? If an invite was already sent prior to running the tool and switching to RCV is the recipients link automatically updated? The internal steps are pretty straight forward. I'm wondering how this works for those who have already been invited with a RCM link. Thanks,