No puller, the tabs you see are probably just part of the optional strain relief. Strain reliefs are good for directing force away from the contacts when cables are under stress but they do not help in protecting the connector when people pull up on the cable instead of the plug.
You can buy plugs with pull tabs but if the connector is as tight as you said then the pull tabs would have just been a convenient method of pulling off the backside of the plug.
If the guys that originally designed the boards were 'nice' about this - they would have used shrouded headers with ejection latches. Flip the latches open and the cable pops out.