I'm pretty sure you have controls at the bottom of your Visitor Messages page that allow you to moderate, delete, etc., VMs on your own profile.

I'm not sure if visitors to your profile will be able to see a moderated VM before it's been approved by the mods, but approving should allow you to read it and clear the notification for you.

I already approved that particular VM so you'll have to try this out next time. The controls at the bottom (and the little checkboxes for selecting messages) should always be there, though. Let me know if that's not so -- I don't see your profile quite the same way you do.