If you opt to require approval for the messages that you supporters send to their officials (set on the Sample Message page of the campaign editor), any administrator set to receive the "service reports and notifications" will receive a daily email letting them know when there are messages awaiting approval. That email will look like this.
To view these messages, log into the admin site, click on the Advocacy menu and choose the option for Campaigns. On the Campaigns page, select the tab for Pending Messages. You will then see a listing of all pending messages, organized by campaign. You can hover over the subject line to view the user's message. You can also click the check icon to approve the message or the ex icon to delete it. If you delete a user's message, the user is not notified of that fact.
If you click the info icon, you will see more message details, including the full text and the list of recipients. If you wish, you can uncheck specific recipients to exercise more granular control over which officials do or do not receive your supporter's message.