The case was brought to the Constitutional Court (ConCourt) by the United Democratic Movement (UDM) with political parties such as the EFF joining the case.
The UDM has argued that it is within the Speaker's prerogative to allow for a secret ballot in a vote of no confidence against President Jacob Zuma.
Mbete had said that it was not within her powers to call for such a vote, forcing the UDM to ask the Constitutional Court to compel her to do so as it was within her powers.
Arguing for the UDM, Advocate Dali Mpofu has faced some tough questions from the full bench of Justices.
Mpofu said they want Zuma to be held personally liable for the costs of the application if the UDM's application succeeds.
Justices spent time asking why the court should entertain the matter and why Mbete was being held liable and not the Parliament.
But Mpofu argued that as Speaker of Parliament, Mbete represented Parliament and she has the powers to call for a secret ballot and so far, she has failed to do so.
Justice Zondo asked why the National Chairperson Of Provinces, Thandi Modise, was not included in the application.
The Justices also stressed their concerns with the UDM's argument that the vote should be done by secret ballot because of a possible "danger or intimidation" of members of Parliament.
Their concern on the part of intimidation, was that it has not been proven, with Chief Justice Mogoeng Mogoeng asking Mpofu to deal with the law.
Political party Agang had asked the Constitutional Court to force the speaker to hold no confidence vote under a secret ballot a few years ago, but that case failed.
That case was referenced a number of times during the UDM's arguments.