A Sydney medical clinic that charged non-English speakers up to $250 for an appointment before their Pfizer jab is giving refunds following media reports.

A GP clinic in Sydney's southwest that charged people hundreds of dollars to receive the Pfizer vaccine appears to be refunding its patients.

But those who paid to receive their vaccine there have been left unsure whether they can get a second dose, after the clinic suggested the government would no longer supply it with Pfizer.

Blessed Health Care, which operates two clinics in the COVID hotspot of Campsie, was widely criticised after AAP revealed it had charged non-English speakers up to $250 for a dose of the COVID-19 vaccine.

The clinic said the charge was for the consultation rather the jab itself. However, COVID-19 vaccines and consults for them are supposed to be free.

The clinic has now asked for the bank details of those who paid to be vaccinated so that they can be reimbursed, Cumberland councillor Kun Huang says.

The Health Department told AAP that the National COVID Vaccine Taskforce would work with GPs and any affected patients to ensure they were reimbursed.

Mr Huang said hundreds of people had joined a WeChat group for patients who'd paid for vaccine consultations at the clinic.

Now the patients are "desperate" because they don't know how to get a second shot, he said.

Chinese-language signs outside the two clinics last week suggested the government may stop providing the clinic with further Pfizer vaccines.

The sign outside the Evaline St clinic said the government was likely to stop providing Pfizer doses to the clinic because of "false" media reporting, but that they would try their best to get enough for the second doses.

At the other clinic, a notice said patients who'd received their first dose there would get their second free of charge, if the government provided them.

The clinics said they were no longer accepting new patients.

AAP asked NSW Health whether the clinic would receive enough Pfizer to dispense second doses. However, the department did not respond to the question.

Health Minister Greg Hunt has said charging for the vaccine was "plain bad behaviour", and promised to "throw the book" at them.

The Health spokesperson said privacy obligations prevented it from disclosing if any practice was under investigation.

Mr Huang called on the state or federal government "to come out and say how they will get the jab".

"We need a process here," he said.

"They should be properly refunded and be sure of getting their second dose."

The receptionist at the Evaline St clinic said "we are busy" and immediately hung up, when contacted by AAP on Tuesday,.

The Anglo St clinic was unattended. AAP has contacted the practice nurse.