Mod mail is empty. There is nothing new in any of the buttons on the right side in my notifications. None of them have a number on them. Clicking on the anyway does not show anything new. Unless, of course, a reply like yours is there but then it says 2 notifications in the top, one in the comment replies, etc.
No, mine was a mod invite. Do a ticket at Changelog ... I had this problem myself once and the admins fixed it in no time. Here's the report a problem link ... it's easy peasy and only takes a minute. BTW, you can put in a faker email, it doesn't care, it uses your username for identity. Link
I had this once when there was a Mod Message that had been sent to me. Look at the sidebar of your user info to see if there may be a Mod Message using the link there. It's not a link that really stands out.