Upon further investigation, now I'm thinking Arca is an older, out-of-use name for O Pedrouzo (?).
It seems that is likely the case. There seem to be three names in circulation: O Pino (or El Pino), Arca (sometimes Arca do Pino), and O Pedrouzo.
Taking this in chronological order, when I look at
El Camino de Santiago: Guia del Peregrino by Don Elias (the fellow who started painting the yellow arrows) and team from 1985 there is no mention of O Pedrouza. What we see is Arca, which is described as the little capital of the municipality of El Pino and is located between Burgo and San Anton (which get bigger entries in the guide book). Similarly,
The Pilgrim Route to Compostela in Search of St. James: A Practical Guide for Pilgrims and Walkers in Spain from 1990 has El Pino on their maps, not Arca or O Pedrouzo, although they mention that free accommodation for pilgrims is available in "Arca (Pino district)". On the other hand, my map of the Camino de Santiago fro the Instituto Geografico Nacional from 1989 shows Pedrouzo (O Pino) and not Arca.
More recently, we see Pedrouzo much more. In Brierly's maps from 2016 he lists "PEDROUZO
Arca/O Pino". Maps and guidebooks generally list O Pedrouzo (although Wise Pilgrim lists "O Pedrouzo (Arca do Pino)".
So my guess is that the regional municipality of that little bit of A Coruna is O Pino (El Pino in Castellano). The capital used to be called Arca in the 80s and before but some time around 1989 or 1990 the name Pedrouzo started being introduced and took over.
Incidentally, I notice that if you search "Arca, Spain" in Google Maps it puts the marker just south of O Pedrouzo, not to far from the Igrexa de Santa Bala de Arca.
Wikipedia mentions Arca not as a town or village but as a parish ("The
parroquias (parishes) of O Pino are Arca, Budiño, Castrofeito, Cebreiro, Cerceda, Ferreiros, Gonzar, Lardeiros, Medín, Pastor, Pereira, O Pino, San Mamede and San Breixo de Ferreiros.").
Perhaps in the 80s Arca is mentioned because it was the parish that provided the albergue and since Gitlitz and Davidson were referring to ecclesiastical architecture in this small section, they referred to it by its parish name. Possibly there wasn't a sign with a place name and when they asked "where is this" people said "Arca" giving the parish name.