Did the parent sign in to the website using the registration code you sent them? You can check that by going Children-->Parent App. If you see the registration code, then you know the parent didn't use it when signing up. If that is the case, you can click the paper airplane icon to resend the registration code.
If it shows the parent has already registered, have them try to log onto the website on a computer and click "forgot password". That will reset their password and email them a link to change it.