Thank you for the advice, Makaveli213.
By the power of Google, I have discovered a way to accomplish what I wanted. I'll post it here in case anyone else is interested:
If you have items in Past Items that are have long ago been removed from the system and want to remove them from the list, use the following procedure.
Click Start > Run > Regedit
Navigate to HKEY_CURRENT_USER\Software\Microsoft\Windows\Curre ntVersion\Explorer\TrayNotify
Delete the IconStreams and PastIconsStream values.
Open Task Manager, click Processes tab, click Explorer.exe, then click End Process.
Still in Task Manager, click File, click New Task, type explorer, then click OK.