I don’t see how this is “least restrictive” if a mass mailing of the concerns to all NYC residents would accomplish the same goal of disseminating the information.
Intuitively, it makes a lot more sense to address the parents directly at the time of the procedure rather than send out a letter that will be thrown out and forgotten. Also, you’re saying that the Health Department should be forced to bear the cost of the risky religious procedure.
Legally, I am not sure exactly how the court would evaluate other potential options. I would imagine that they do not expect every mandated disclosure to be sent out by the Health Department.