Who Tends to Chalice Spills?

. . . If any of the Precious Blood is spilled, the area where the spill occurred should be washed with water, and this water should then be poured into the sacrarium in the sacristy. (GIRM, 280)

There is nothing there that states this is the exclusive domain of the clergy. Should the parish priest want to reserve this action to himself to ensure it is done properly, that is certainly his right; however, there is nothing that states he cannot permit an EMHC to do it.