If you don't have the email address of someone you need to invite to the group, simply send them the URL of your Pay By Group. Each Pay By Group has a unique URL. This URL isn't indexed by any search engines, so you'll need to share the link with someone directly in order for them to find it.
For your convenience, the "Copy URL link" button on the dashboard will automatically copy the group's link to your clipboard. Simply give this link to the person you need to invite via any medium you like.