The hotel maid is kind of like the padrone's attendant fairy—his Tinkerbelle. She has a way of simply appearing: popping open the umbrella at the door and arriving with the cat from the padrone with curiously good timing. She's a little doubtful that there's actually a cat in the rain, but she still goes out with the umbrella and remains attentive to the wife.
The small detail of the maid staying outside to close the umbrella while the wife passes inside is a wonderful representation of how dedicated she is to her job. Like the padrone, she takes this service very seriously, no matter what her own thoughts are.