Hi Joy,
The Voice system has loads of websites, and the idea is that users can be a member of Voice, and then independently become members of individual sites within the system.
So, although these members are not in your site's list, they are probably already members of Voice, which is why the site says that they can't join again.
Because your site is configured to have a private membership (users require an invitation), the way to get them onto your site is to go to the Users & Permissions page, and at the bottom of the list of members click the "Invite others to join" link.
You can add their names/email addresses on this page.
The invited users will be sent an email asking if they want to join your site, with some instructions of how to do so. If they are already users of Voice they they will just have to click a link to join your site. If they are not already Voice users then they'll have to register.
I hope this helps, and sorry for the incredibly slow reply! I'll be faster next time...
Joe - Voice Admin