A comparison between the 1981 Missale Cartusiense (available for download online!) and the former Carthusian Mass, as detailed in A.A. King's 1956 Liturgies of the Religious Orders (a facsimile of which I own), shews that the monks of the Charterhouse have made but few changes in their manner of offering up the Sacrifice.
In general, these wise sons of St Bruno have adopted and adapted some few modern Roman revisions, but have maintained their distinct, settled Use better than all other reforming liturgists. This may well be because the Carthusian Mass was always the most spare and simple of the many different ways of celebrating the Roman liturgy, with an entire absence of unnecessary ceremonial, and so had less to be messed with!
What changes have they made?
At the start of Mass, they have transferred the sign of the cross, still made secretly, not aloud, by the priest, from before the Introit to become the very first words of the liturgy, and likewise have moved the Dominus vobiscum from before the Collect to directly after this In nomine... – these modifications clearly parallel those made to the Roman Mass.
They have removed the curious choice of versicle formerly used before the Confiteor – the Pone Domine used in the Traditional Roman Mass during the censing at the offertory – and replaced it with the more apposite versicle Adjutorium nostrum that they used to say after the Misereatur.
Their Confiteor they have lightly revised inasmuch as they have changed from confessing "to blessed Mary and all the saints" to asking their prayers – which if anything is a distinct improvement. Now, too, as in the Novus Ordo, all say the Confiteor together. It may be noted that the Carthusians have always said the Confiteor &c. aloud and before the singing or reading of the Introit.
Finally, instead of the former Pater and Ave before going up to the altar, there is now a rubric specifying that the priest should pray in silence for a time.
The rest of the fore-Mass remains much as it has always done, with an Epistle, Responsory (Gradual), Alleluia and Gospel; a Lesson before the Epistle, to make three readings in all, is only used at the Masses of Christmas, as in the Dominican Rite.
What of the Offertory? If Mass is not sung, the Offertory antiphon is omitted. The Dominus vobiscum and Oremus have been suppressed; the In nomine... at the end of the formula for mixing the chalice with wine and water has been dropt; the Orate fratres has been changed back to its primitive form of those words alone (there was never a response to it, other than the heartfelt prayers of those around, in the Carthusian Rite); the Oremus before the Prayer over the Gifts (formerly known as the Secret) has been removed as a doublet of the Orate fratres. The Prayer over the Gifts now has only the short ending. That's all.
What of the rest of the Mass, the Consecration and Communion? The three new Eucharistic Prayers from Rome have been introduced as options, and, if Mass is concelebrated, the Prayer used is to be said aloud (how else could it be done, after all!). The modern text of the Embolism (the Libera nos) has been substituted for the old, but without its strange doxology. A short new prayer for peace, Dómine Iesu Christe, da nobis illam, quam mundus dare non potest pacem – this seems the least happy innovation, and a needless redoubling of the prayer for peace in the Embolism! – has instead been sandwiched in between it and the Pax Domini. Pretty clearly, the Fathers were under some pressure here and had to compromise...
The strange Carthusian manner of singing or saying only the first petition of the Agnus Dei before communion, and then singing or saying the other two afterward, has been abolished. A rubrick directs that the priest prepare either by a short meditation for communion, or may say either the traditional version of the Domine Jesu Christe, Fili Dei vivi... or the Roman Percepti Corporis et Sanguis... – and the words of administration are changed to the Novus Ordo's short form as well. Contrariwise, the Charterhouse monks have retained the use of the long ending for the Prayer after Communion, which the modern Roman Mass kept only for the Collect.
These changes, so far as I can tell, are the only ones made to the Carthusian Mass since Vatican II and all that.
The Order still retains such special variants as its own wording of a phrase in the Gloria in excelsis: they read propter gloriam tuam magnam, "for Thy glory great", emphasising how boundlessly great is the glory of God; so too the Creed in the Use of Chartreuse still retains a variant phrase at its end: et vitam futuri sæculi, "and the life of the future age" – very appropriate for an assembly of monks trampling upon the passing things of this world, and looking forward to the true life. In both these cases, as the Order retains and sings its proper plainsong still, no change could be made without affecting their chant.
For interest's sake, here is the Carthusian suite of offertory prayers (NB their rite never had the Suscipe sancta Trinitas so commonly found in other Uses):
When the priest puts water into the chalice, he says:
De látere Dómini nostri Iesu Christi exívit Sanguis et aqua in remissiónem peccatórum.
When he washes his hands, he says:
Lavábo inter innocéntes manus meas, et circúmdabo altáre tuum, Dómine.
And he adds two or three of the following verses:
Ut áudiam vocem laudis, et enárrem univérsa mirabília tua.
Dómine, diléxi decórem domus tuæ, et locum habitatiónis glóriæ tuæ.
Ne perdas cum ímpiis, Deus, ánimam meam, et cum viris sánguinum vitam meam.
Standing before the middle of the altar, the priest offers the chalice with the paten on top, holding them elevated, saying secretly:
In spíritu humilitátis et in ánimo contríto suscipiámur a te, Dómine, et sic fiat sacrifícium nostrum in conspéctu tuo hódie ut pláceat tibi, Dómine Deus.
And he makes a cross with the same chalice, saying:
In nómine Patris, et Fílii, et Spíritus Sancti. Amen.
He replaces the chalice on the corporal, and the paten in front of it, containing the bread to be consecrated. He covers the chalice with the farther part of the corporal [this is the universal ancient use, prior to the development of the pall].
If incense is to be used [at the Conventual Mass], the priest, having poured water into the chalice, at once makes the oblation. Then he adds incense to the thurible and holds this lifted over the oblations, saying:
Dirigátur, Dómine, orátio mea, sicut incénsum in conspéctu tuo.
Then he censes once over the oblations in the form of a cross with these words:
In nómine Patris, et Fílii, et Spíritus Sancti. Amen.
And once in the form of a crown, and then, toward the cross, to the right corner, to the left corner, and thrice lower down before the front of the altar. Then he returns the thurible to the deacon, he washes his hands and stands with joined hands at the altar corner, turned facing the cross, until the deacon has thrice censed him;then before the middle of the altar he remains with folded hands until the deacon has gone round about it [censing].
When he turns to the people he says:
(The Prayer over the Gifts follows.)
I have noted below that the Carthusian Mass still ends with the Placeat sancta Trinitas.