As the city prepared a waiver application yesterday for Mayor Bloomberg’s controversial pick to head the public-school system, dozens of protesters tore into his choice of someone with no background in education.

Bloomberg plans to apply this week to state Education Commissioner David Steiner for permission to hire media mogul Cathie Black.

But protestors outside the Tweed Courthouse yesterday said they were sending Steiner letters demanding that he not grant the waiver — needed because Black lacks the required educational qualifications to be chancellor.