Thanks for jumping in here.
For sure, it happens with Windows Explorer. Click on the close button, and
up comes IE!
Now, here's a possibly connected anomaly. I downloaded an update of
RoboForm. During installation, it kept begging me to close IE. But IE wasn't
open.
I terminated explorer.exe from the processes list, and the Roboform
installation finished. But explorer.exe is listed as Windows Explorer, not
Internet Explorer.
So there seems to be some nexus between the two that I don't understand.
Maybe I ought to uninstall and reinstall IE7?