Traditional Latin Mass/Gregorian Masses
Gregorian Masses do not necessarily affect the liturgy in any way as they refer only to the priest's intention in offering the Mass. There are no special rites or formulas attached to Gregorian Masses.
One point, however, that Gregorian Masses are rarely celebrated in parish settings. This is not because of special rites but because a parish priest would find it very difficult to dedicate 30 days of Masses for one single intention, especially when many parishioners request Masses.
Therefore Gregorian Masses are usually celebrated in monasteries, seminaries, priestly houses of studies, and other similar locales with priests in residence with relatively few pastoral commitments. These are usually the only ones who can take upon themselves the commitment to celebrate 30 consecutive Masses for the same deceased person.