I don't use McAfee anything, but I found this:
<a href ="http://72.14.207.104/search?q=cache:jJvG8oJ-QYEJ:static.tigerdirect.ca/pdf/McAfee_AntiSpyware_UserGuide.pdf+%22McAfee+Privacy+Service%22+options+%22activity+logs%22+faq&hl=en&client=firefox-a">Google cache file</a>. In it, it says there is an option, at least for the anti-spyware component, to click a "Recent Activity tab" and then you can set stuff like to delete the logs.
Edit: Oh, I just read you are using your parents' PC and don't have full access, so that might not work. If you don't have search access on that PC, and if it's really locked down you may not even have delete access of the log files once you find them, then I recommend getting a <a href="http://www.knoppix.org/">Knoppix</a> CD with NTFS-write (if they use FAT32 then that's no problem!), and just searching for the log files at prompt (*.log on /mnt/hda1), and then deleting those that you need to delete.
That ought to work I think.