How can I automatically reject new Cases submitted by a Contact who is not enabled as a Portal User?

We have a set number of Users who have permission to log into our Portal per client. In this example, let’s say we have Company X with User A, User B, and User C. Only these three Users can log into the Portal to submit tickets. They can also email our Support email address to submit a new Case. Unfortunately, this also means that anyone emailing our Support can submit tickets despite whether or not they are set up in the Portal. Does anyone have any suggestions on how to automatically reject Cases submitted by individuals who are not configured as Users? I’m sure we could create a Business Event but I’m not sure what conditions we would need. Any help is appreciated!