I don't know, to be honest. If monstergirls are something that shouldn't exist in the world of our game, where did these interested third parties get them from? I personally think it will be easier to say that the third parties seek out the potential monstergirl masters with a deal and, after having signed a contract/made a deal, they'll show/help the potential summon their monstergirl. We could say that the potentials are the only ones that can summon a monstergirl and thus participate in the grail tournament because they have a unique innate energy, one that attracts the monstergirl to form the bond with them and that said monstergirl needs to feed off for energy (normal human energy would be considered much, much weaker compared to that of their summoner).