In order to allow non-TCNJ Users to your Google Group, you need to first enable that option by following these steps:
How to Enable External Members
- From your Google Group, go to the "Settings" Section
- Scroll down in the "General" section you start in and you will start to see options regarding who can join the Group
- Under "Allow External Members" select the "On" option

After checking that box, you must click the save button. You will be able to use the "Invite members" and "Direct add members" options to add members outside of TCNJ.