90% of the time this happens because the email they used to sign up for Cc is not the same as the email you used to invite them. Ask them to log in and check which email they used (to check, have them go to their home screen, and then select ‘Account’; they will see their email listed), and then go back to the group on your computer and make sure that:
Either way, you'll need to re-invite them. Once you do, their name should pop up in blue letters. They will just need to refresh their page and the will see the group!