The story is that St. Gregory added the latter part of the Hanc igitur to the Canon. That is found in the Liber Pontificalis. But the people rioting is a pious belief of the Middle Ages. And he was by no means the first to change the Roman liturgy.
Other changes to the Mass include the Kyrie (which on weekdays was in the the form of Kyrie…Christe…Kyrie instead of a litany), singing Alleluia outside Easter, and the shifting of the Our Father from the Offertory after the Canon and before the fraction. Many scholars also theorise the shifting of other parts such as the Pax, and even the Memento of the Dead. (See
here for the letter of St. Gregory)
Of that period there are no things that tell us what the liturgy was like except what is written in the letters, and what the Liber says. The three major (and large) books (should I say families for the latter two?) of liturgical texts are
The Leonine Sacramentary - it was supposed to date from the time of St. Leo the Great but now a lot of scholars say it is closer to the seventh century. It is a collection of prayers for Masses-somewhat more like a prayerbook-and it doesn’t have the Canon
The Gelasian Sacramentary: this is a hybrid Roman-Gallician liturgy. And it gives the Canon almost as it was until recently-there is variation for the saints and the Memento for the Dead is missing. The book does not go back to Pope Gelasius despite it’s name: one manuscript has Masses for the exaltation of the Holy Cross and the Canon and the Lord’s Prayer are in the position of St. Gregory. And elsewhere there is an exhortation given attributed to Pope St. Gregory.
The Gregorian Sacramentary: these are based on a manuscript sent by the Pope Hadrian to Charlemagne in which he says “As to the Sacramentary drawn up by our holy predecessor, the godly Pope Gregory, Paul the grammarian asked us on your behalf to send you a pure text,
according to the tradition of our holy Church, so we have sent one to your royal excellence by John a monk and Abbot of the city of Ravenna…”. In the older manuscripts there is a first part which is supposed to be the original work and then supplementary material in between there is a preface in which the writer mentions St. Gregory. In the later manuscripts the sections are not delineated.
The above is a gross oversimilification so if you’re interested in the analysis, you can read Bishop’s
here
Some of the manuscripts you can find
here (Veronese is the Leonine)