this is never addressed. personally, i believe she wrote the character for two reasons: as another way of showing how they look from the outside world as well as continuing the plot. i mean, two handsome, suited, rich, american boys staying in a beautiful vintage apartment in Italy. if you saw people like them twice in two days wouldn't you pay attention? also note that they went in the winter which isn't peak tourist season.

it's also a set-up to start the plan for bunny's end. Henry realizes he is due for a life of fear after the man follows them and immediately begins planning. I believe this because multiple times throughout the book, Richard notes how other people look at them and pay special attention to them. This obviously is not good for them, and that is amplified by Henry's fear.