Charter school advocates are jumping at the opportunity to use Chancellor Carmen Fariña’s words against her.

Dozens of parents with Families for Excellent Schools gathered at City Hall on Tuesday and said they wanted Fariña to apologize for saying that some charter schools have illicit enrollment practices. They specifically latched onto one of Fariña’s more provocative claims, that charter schools violated admissions requirements by recruiting top-scoring students using “postcards.”

“Show us the postcard,” they demanded at the protest.

Fariña’s exact comment was that charter schools shouldn’t just accept “kids who get postcards because they’re level 3s and 4s to come to the school.” She also suggested that charter schools counsel out students before state tests in an effort to inflate scores, another claim that charter school advocates have rejected.

Fariña also said charter schools should do a better job of serving students with disabilities and English language learners, a critique that even charter school leaders have acknowledged has merit.

Families for Excellent Schools CEO Jeremiah Kittredge said the rally was focused on Fariña’s most provocative comments about student recruitment because they were “patently untrue” and less on enrollment equity. But he also said he thought charter schools were serving “equal, if not more, special needs and ELL students,” a view that is not supported by enrollment data.

While some schools do serve higher-than-average numbers of special needs students, the average charter school does not, according to the New York City Charter School Center. Whereas charter schools serve 15.7 percent of students with disabilities and 6.2 percent of English language learners, district schools serve 18.2 percent and 14.3 percent, respectively.

Coupled with Fariña’s refusal to retract any part of her comments from last week, the rally is one more example of how little ground opposing sides seem willing to concede in the divisive debate over charter schools. That debate is likely to intensify in the coming months, when lawmakers are expected to consider lifting a cap on the number of charter schools allowed to open in the city.

One thing that many sides seem to agree on is that more information is needed. United Federation of Teachers President Michael Mulgrew and New York City Charter School Center CEO James Merriman have both called for the city to release data that would shed more light on how often students are leaving charter schools compared to district schools, and if their churn is happening at certain points in the school year to support Fariña’s claims.

So far, the Department of Education hasn’t said if it would release the enrollment data being requested. In response to Tuesday’s rally, a spokeswoman said Fariña’s comments last week “gave voice to concerns that parents and a diverse range of stakeholders have raised.”

Two state education agencies suggested on Tuesday that settling some parts of the debate was within Fariña’s power.

The city “has the most accurate data on mobility” for charter schools, said David Doyle, a spokesman for the State University of New York, one of two organizations that authorizes new charter schools. The other authorizer, the State Education Department, analyzed its own city student mobility data last year, but found it “somewhat challenging to interpret the results” because the city keeps records in a different way.

“Our analysis was more back of the envelope and not sufficiently rigorous to share with the public,” said an SED spokesman, Dennis Tompkins.