Here's what I would do:

Go get Roger Zander's Client Center
(http://sourceforge.net/projects/smsclictr)
Once installed, connect to that test box, go to the Advertisements (bottom
left)
Show Assigned advertisements.
Find your advert.
right-click, rerun advert.

Of course, if you've *just* changed the ad in the console, the client hasn't
picked up the changed policy yet; so you'll have to watch that what you are
re-running is your updated ad/package/program (but back on SMS Agent Actions,
you can have the client Download policy, wait 2 min, Apply Policy, to
encourage that along)

There's other ways to remove the history of a particular advert (it's just a
regkey assuming this is a computer-targetted ad, not a user targetted ad);
but you're frankly missing out if you don't have Client Center.

Oh.. if you do target users or usergroups (your collection contains
usernames or usergroup names, not machine names), almost nothing works.  
Although Stuart Watret has a right-click extension for SMS2003 (doesn't work
w/ConfigMgr; at least I don't think he's updated it) to re-run a user based
ad.  http://offshore-it.co.uk/  So you could use that.  It's slightly
painful, but it's better than nothing, or trying to find the goofy thing in
WMI & delete the policy.  That's excruciatingly painful.