In theory, given that it's purely organisational and only marginally religious, the top Authorities are the Archbishop, the local Chief of Police (at a stretch the Interior Minister, the PM, and the King -- but that would be
seriously pushing it beyond the very local and individual nature of the affair), and the Mayor.
De facto, neither the Holy See nor the Pope are responsible for the Pilgrims Office, although both could if they wanted exercise some extraordinary oversight upon it.
More realistically, the top man for some disciplinary affair of this sort is the boss of the Pilgrims Office itself :
https://oficinadelperegrino.com/en/pilgrims-reception-office/
The Pilgrim’s Reception Office is run by the Cathedral church of the Archdiocese of Santiago de Compostela. The Director of the Pilgrim’s Reception Office is traditionally a Canon of the Cathedral. The present Director is Segundo Pérez López.
And yes, his Boss is the Archbishop ; except if he reports to the Vicar General instead ; or to the Archpriest of the Cathedral Parish, if there is one. The supervising Office is anyway that of the Cathedral Parish rather than the Episcopal Palace.
Common rudeness is however hardly a Police matter in Spain, unless it amounted to
serious incivil behaviour ; which realistically, this behaviour does not.