"1 alert" is on the next to "About This Mac"
I have macOS Mojave 10.14.6 on my MacBook Pro (2017, 15-inch), and I see the same message, which persists after rebooting.  I do occasionally run CoreServices apps directly.

I'm no systems expert, but it makes me think that:


A CoreServices app added itself to a startup folder upon first launch.  (e.g. the LaunchAgents, LaunchDaemons, or Startup Items folders in one of the Library folders)  It may also show up in the Activity Monitor.
A Terminal command may reveal alerts that can't display in About This Mac screens.  (I tried "mail" for my own account, but there were no messages.)