I imagine some of the English speaking readers do not recall having heard a “song of peace”. I have seen that in many of the latin-American Spanish Masses: after the Our Father comes the rite of peace, then a song, such as “
dame la mano” (give me your hand [see full lyrics below

]), and when the people have calmed down or in order to calm them down 'cause otherwise they won’t, the cantor rapidly switches into singing the Lamb of God…
…I guess this would be an example of what the Holy See desires to change.
*No importa de donde tu vengas
Ni tu raza ni cuanto tu tengas
Si en tu corazon tienes a Cristo
Dame la mano y mi hermano seras
Dame la mano, Dame la mano
Dame la mano y mi hermano seras
Dame la mano, Dame la mano
Dame la mano y mi hermano seras*
Translation:
*I don’t care where you come from
Nor about your race or how much you have
If in your heart you have Christ
Give me your hand and you’ll be my brother…
*
Needless to say, the tune isn’t any more suitable for liturgy than the lyrics…