The first legal challenge against Hecht-Calandra was launched in 1974. Only 3 years after the law was passed. Since then there’s been a number of legal actions.
Here’s one from 2007.
A public-interest law firm in Washington filed a class-action lawsuit against the New York City Education Department yesterday, charging that a program created to increase the number of black and Hispanic students in the city’s elite specialized high schools violates the Constitution by excluding whites and Asians. The law firm, the Center for Individual Rights, filed the suit in Federal District Court in Brooklyn on behalf of three Chinese-American parents whose children were denied admission to the Specialized High School Institute, which prepares students for the test determining admission to schools like Stuyvesant and the Bronx High School of Science.