When I finished the Primitivo in Sept 23, I spent 12 euro in Santiago to post a bunch of unused materials back to the municipal albergue in Oviedo, with a brief note in Spanish that said, For the next pilgrim. Correos provided the box.
It's not at all economical for there to be a pilgrims office in Madrid, since so few of the recognized Caminos start from there. Although many pilgrims may fly into Madrid, most of them go somewhere else to start their Camino, and many more tourists fly into/ through Madrid than pilgrims. They have no need of our leftovers.