You do not say what mail system you are using. Is this Exchange? If so what version and service pack level? You can set a restriction on who can send to the DL in Exchange. How to do this depends on the version. You restrict all users from sending except the approved users. This is what we had to do to prevent company spamming from internal email users. Trust me when they get the bounce back that they do not have permission to send to the DL they will call your help desk and the help desk will refer them to the approved sender. They can then send the email to the approved sender for review. You could also send out an informational email first letting everyone know who to send their email to for approval. I know of no automated way to do this process. It has been working well for us for 4 years this way.
Thanks Technochic, this answer helped. I snooped around.
Under AD> Properties of the Broadcast List > Exchange General Tab > Message Restrictions > Select Only From> Add Users to the list.
And you can Add the user who can screen it before it is re-sent out.
If user who is not permited tries to send and email to this Broadcast group you get a ‘You do not have permission to send to this recipient. For assistance, contact your system administrator’ Email back from the System Administrator.
Which brings me to my next question, how can I change this message so that a user knows what is happning and why permission to send an email was denied.