Our villa in Jamaica is equipped with 2 computers on which I dare not enter any personal information. I just spent about an hour working on clearing some disgusting spyware from a system running Windows Vista Basic. Even after updating Firefox, the same windows keep popping up. First thing I tries was to uninstall Firefox. Which solved the problem in an unsatisfactory way.
Since the infection was limited to the Guest account, I thought "I'll just delete the Guest account".
Apparently, that is not possible. Seems pretty dumb. Thankfully, it can be disabled. So I disabled the built in Guest account, reinstalled Firefox and and created another regular account, which can be deleted and recreated as needed. Problem solved.