You can choose who has access to email-in a message to a group, or shut the service off, from the Custom Email Options on the Group Settings page:  

To get there, go to the group page and click on Group settings

Scroll down and expand the Custom Email Options and then find the EMAIL RESTRICTIONS section:

Restricted email-in access: This selection allows only users who are in your network email-in to groups 

Unrestricted email-in access: This selection allows users who do not belong to your Regroup network to post a message to the group, as long as they have the email address for the group. This can be useful for community outreach notifications and for emergency response coordination.

Disable this feature: This selection disables the ability to email-in a notification to the group completely

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