How to get rid of Fake McAfee Notifications NOT running McAfee

If, as you suggest, your husband picked this up from a visited web site, then I suggest that you download, install and run the trusted free app Malwarebytes It should eliminate the problem. Click on the link below to download it.

Malwarebytes

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

The other possibility is that Mcafee has been installed in this computer sometime ago and then later removed. However, if the app was not removed using the Mcafee uninstaller, all of it might not have been removed. You can try reinstalling it and then using their uninstaller which will remove all of the app's bits and pieces. If this is the case, it will then stop those notices.