Ping
I think that what happened was probably that the priest was saying these prayers after all of his NO masses and Cupich caught wind of it.
They were required after all low Masses prior to VII and the NO mass, but they were suppressed then and hence are not part of the NO mass. Technically, saying them counts for adding a part of the Old Mass to the NO mass, which is forbidden. So I think Cupich told him to stop saying these prayers publicly after his (NO) masses.
It’s still a prohibition, but Cupich can claim that he didn’t stop the praying of these prayers but was simply guarding the “purity” of the NO liturgy, Notice he mentions something about that in his letter.
Therefore, he was able to force the priest to say that the priest “misspoke.”