Displaying new results currently being filtered out

I'm currently working on a messaging tool and one request was being able to filter the conversations by (Internal Team / Customers / Flagged)

One thing we're running into is what happens when a new message comes in that is currently being filtered out...and it might be a customer that needs a quick response.

One thought is to display a small banner at the top of the inbox stating that "1 New message being filter out"...but we also don't want to annoy users that are aware that the filter is blocking the incoming results.

Any suggestions appreciated. Thanks