Walt,
The "hands-on" method:
That MRU list is in the registry at

[HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\ Explorer Bars\
{C4EE31F3-4768-11D2-BE5C-00A0C9A83DA1}\ FilesNamedMRU]
and
[HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\ Explorer Bars\
{C4EE31F3-4768-11D2-BE5C-00A0C9A83DA1}\ ContainingTextMRU]

Run regedit (Start> run> (type in) regedit) and make your way to those keys
and remove all (string value) entries in the right pane except "default."

After you clear those keys, export them (as REG files) and doubleclicking
either of them will clear that list again whenever the need arises. You'll
be merging the empty keys back into the registry and replacing the "full"
keys.

Please export the registry before doing this. As soon as the regedit window
opens, select My Computer then Registry then Export. Should you wish to undo
a change, dbl clicking that REG file will restore the previous registry.

Regards,
Don