Only the reunion organizer can invite someone to a reunion directly. If someone isn't on the reunion's invitee list, you can contact the reunion organizer and ask them to send the person an invite. From the event page, look for the Contact option next to the reunion organizer's name.
Please keep in mind that only registered Classmates® members affiliated with the school and grad year(s) included in the reunion event can be invited using the website. If you'd like to invite someone who isn't currently a member, encourage them to register as a free member and they'll automatically be added to the invitee list for any future reunions their class is invited to.