Rae Ellen, the story of this battle between the Tessiers and the Sulpician priests has just about as many versions as there are descendents of Urbain Tessier and Marie Archambault. The long and short is that the Grey Nuns had nothing to do with the legal fights. It comes down to the Last Will of Marie Archambault which left the land to the Sulpicians. Over 100 years after her death, some heirs tried to argue that she only left the land for the Sulpicians to use under the basic equivilent of a 99 year lease. The Crown interceded and found on behalf of the Church. Then in the late 1920s, after yet another 100 years, a few heirs tried to revive the suit again. Again it was dismissed as being without merit.
There have been several appeals and even more attempts to resurrect the suit in the last 70 years. None of it will go anywhere, as the legal premise they're seeking relief under was settled as a matter of law almost 200 years ago. The rumors about "disappearing" papers which would change the whole suit and prove the heirs are legally entitled to the land under Notre Dame and one of the largest banks in Canada is urban (or in this case Urbain) legend. But following it won't take you closer to the truth. Somebody made loads of money trying to pursue this, but none of them were actually descended from Urbain and Marie.