Mass (and Holy Communion) quoad se (intrinsically or in and of themselves) have infinite grace.  One Mass has enough grace to convert the entire world, and one Holy Communion to turn the most abominable wretch into a the greatest saint.

But not ALL of this grace transmits to or gets applied to souls.  So, quoad nos, the amount of grace we receive depends on God's will.  Nor is it necessarily just proportionate to the dispositions of someone receiving Holy Communion.  So, for instance, saints have said that if an unworthy priest offers Mass, even if it's valid valid, let's say the priest is a grave sinner, a sodomite, child rapist, etc., then the amount of grace from the Mass that gets applied to the faithful is much less, if any.

So the difference is between intrinsic grace, and applied grace.

If a Satanist priest says a Black Mass, even if valid, I doubt that any graces will flow from that into the world.  Instead, it's quite the opposite.

If a Catholic went to a Greek Orthodox Liturgy to receive Communion (let's say he didn't know that was wrong and committed no sin, subjectively speaking), there's nothing that says God has to apply the graces of that Communion to the recipient's soul.

There's no theological principle that dictates that God must apply grace from the Mass or the Sacraments to a soul at all, any more than there is a principle that God needs to apply 100% of the grace (if it weren't infinite and could be thus quantified).

So, again, assuming that 100% is the amount of grace intrinsically available from a Mass, God could dispense / apply 80%, or 50%, or 10%, or 3% or ... 0% of the grace.  Johnson's misguided theory would hold that there must be grace given.  So if God dispensed .000000000001% of the grace, that would comply with his made-up principle.  We know that God does not dispense all of it.  So, perhaps Johnson could come up with some math about how much grace God is bound to bestow.

Does the New Mass gives grace? Abp. Lefebvre said it is sterile and doesn't pass the grace. A sacrament is defined in the traditional catechism as "an external sign, instituted by Christ, that gives grace." This is presupposing the "sign" is a Catholic sign, and not tampered and modified to give a Protestant and Modernist expression. The New Mass expresses a sign that is no longer Catholic, but Modernist. This is because the New Mass incorporates some Catholic elements, some Protestant elements and some Modernist elements, all combined into one liturgical action. So, taken as a whole, the sign expressed in the New Mass is a Modernist sign, a Modernist Liturgy, one that no longer expressing the Catholic Faith!

Consequently, it can be debated at the theological level if this New Mass, expressing a non-Catholic sign, actually confers grace, even if it be valid at times. It appears Abp. Lefebvre never thought it did. Bp. Williamson holds that if it is valid then it automatically gives grace. Perhaps, one could argue that POTENTIALLY it could give grace (if it's valid), but ACTUALLY it doesn't, in many cases, because of the lack of dispositions necessary. This, because the priest and many attending the New Mass, have a non-Catholic understanding of the Mass, and if it's merely a "symbol of the faith of the community," as is taught by Modernists, then their lack of Faith and proper dispositions, blocks the transfer of grace in their souls. In this case, for many souls, the New Mass doesn't give grace.

As I said, perhaps there's room to debate at the theological level, but at the practical level, it is extremely dangerous for clergy to promote the erroneous opinion that "the New Mass gives grace" because uninformed souls will take this as a green light to attend it and put their Faith in grave danger! Even Abp. Lefebvre said that he believed the New Mass doesn't fulfill the Sunday obligation, precisely because it expresses a different Faith from Tradition. "Lex orandi, lex credendi," as the axiom from St. Vincent Lerins says, "as we pray, so we believe." If we pray as Catholics, we will believe as Catholics; if we pray as Protestants and Modernists, we will believe as Protestants and Modernists!

I have never condemned Bp. Williamson, who I respect and honor as a seminary professor and the bishop of my ordination, but yes, I have publicly warned souls against the erroneous opinions that he promotes because it is contrary to Abp. Lefebvre's position and for the obvious danger such a message presents. As Fr. Carl Pulvermacher, O.F.M. used to put it, "Do you need proof the New Mass doesn't give grace? Look at the catastrophic fruits! There's your proof! As Christ said, 'By their fruits you will know them.'"

Apologies, M. Ladislaus, but the previous post was written by me (I forgot to check the box, and when I tried to do it after the fact, I was not permitted).

In any case, if I understand you correctly, you think to evade the Tridentine anathemas by interpreting "receives rightly"  as pertaining to the rite of Mass used to confect the sacrament, rather than whether or not the communicant is in the state of grace.

Is this correct?