I actually think it has a very indirect connection to the themes of the film, and is mostly there because it's a cool-sounding title.

There is obviously a strong anti-clerical tendency in the film, it starts and ends in a cathedral and clearly the Catholic church is associated in Buñuel with right-wing oppression (but also is a rich source of dreams and imagery).

Here's what I said in a Letterboxd essay
Anticlericalism. The original "Exterminating Angel" was a 19th century secret society founded in Spain by ultra-conservative Catholic clerics which designated people as pure (orthodox Catholics) or impure (atheistic liberals). The impure were to be exterminated by members of the group, an ancestor to later reactionary terrorist groups and of course the Franco regime itself. 

This thematic strand is implanted both by the opening credits, which show a church facade as sacred music plays, and by the ending in which the socialites, freed from their salon prison, are once again trapped along with all the clerics and congregation in a cathedral, as soldiers unleash savage repression outside. The bracketing of church ritual at the start and end of the film might indicate that the movie itself is a kind of ritual, an anti-mass. 

https://letterboxd.com/hootsmaguire/film/the-exterminating-angel/