IANAL, but I did a little research before getting started in lock picking a while back. iirc, there are no federal laws against having picks. However, states often have laws against "possession of burglary tools". In my jurisdiction, if they can establish intent to burglarize -- ie, you're also carrying an empty duffel bag, a crowbar, and a map with the bank circled on it -- its a class II felony.
I repeat; I am not a lawyer.
In the same way you can have a big knife at home but carrying it in your bag is a problem.
I used to carry a similar card. It was a fake credit card that opened up, and had a small set of picks inside. I kept it in my wallet in case I was ever locked out.
In it this very issue is addressed including the advice "It may be a good idea to carry around a xeroxed copy of the appropriate page from your state's criminal code."
Problem solved.
That's a line that'll generate hours of debate going nowhere.