Hi Big Ed,
Since you mentioned the Button, I assume that you are interested in how to
do this in Word 2007. You can remove all the files that no longer exist from
the list. To do this, click the Office Button, click Word Options, click
Advanced, go about half-way down the list of options, set the number in the
Display this number of recent documents option to 0, and click OK. At this
point the list will be empty. Then go back and set the number to its previous
value or to another number that you prefer, click OK, and click the Button
again. The files that still exist will be restored to the list.
If you want to list empty the list completely, follow the same procedure,
but close Word before you click the button the last time to see the restored
list. You can also empty the last n files in the list by setting the number
to the current number minus n instead of 0.