this is entirely my own guess, internalizing what I remember from preparation for consecration, is that this refers to changing our own attitude toward prayer and about prayer. Maybe we tend to think “I am praying for you, I will pray for you, I have prayed for you” as actions that belong to me, initiated by me, and are efficacious because of what I did, my intentions, sincerity, fervor etc. If we can achieve the sate he is refering to, we would no longer refer to “my prayer”, “my sacrifice”, “my good intentions”, “my best wishes for your good health,” “my efforts to help the poor,” “my donation to the work of the missions.” and so forth. we would speak of anything we happened to do as work undertaken with, in and for Christ through Mary, not as anything we have initiated and accomplished, but as participation in Christ’s prayer to the Father, Christ’s mercy, Christ’s healing.
We would no longer a pray in a manner that gives orders to God, but in a manner that has as its only goal conformity with God’s will. We would never again pray in a way that seems to dictate to God what the best outcome would be. And we would never again do acts of charity in a way that is reprimanding God (for letting the evil exist in the first place, and thinking we can do better than He can in putting things right). that’s just my best guess.