Could they do that? You'd probably have to read (and keep up with) the T&Cs.
Or worse. They get access to those Facebook Messages?
Add the representative of the bank to one of the limited visibility groups.
Not sure how that works when FB API is used.
Alternatively, if you are genuinely worried about being able to do this, I would advise setting up a public profile separate from a personal one (cpt obvious).
I remember when it was a faux pas to put your real name on the internet - long live the days of having an alias that you can make a whole bunch of mistakes to a private group of friends without being publicly remembered for it.
I seem to remember a lot of articles about that and then it just stopped.
A rare outbreak of common sense in US labour law, although I suspect Facebook also lobbied for it - it's against their TOS to give your credentials to the interviewer.
Same as for us foreigners who don't have any credit rating records valid in US. Meaning you get the crappiest deals and worst apartments.