It's my office computer, so I have what they say I can have.
I did try this on my home computer (also XP Pro, SP2) and get the same symptoms.
I'll try to investigate further.
[investigates]
I understand now.
1. Cleaner mode does more than just delete files. It does work over the registry as well.
2. The registry keys in CCleaner's WinApp.ini file for WinZip do get deleted when Cleaner is run, which "resets" my settings to the defaults the next time I open WinZip. (I don't agree that those particular settings should be deleted, but it appears I can change it).
Thanks to all for your help, and esp the info on the ini files.