A Muslim lady has gone to the kuffaar court for getting divorce.

Answer

Perhaps you are mistaken. The lady could not have gone to the kuffaar court to gain Talaaq. If she is a Muslim, she will know that the kuffaar court does not issue Talaaq. Also the court will not entertain her request for Talaaq because the court knows that it is not empowered to issue Talaaq. Furthermore no lawyer is so stupid as to apply to a kuffaar court for a decree of Talaaq. The court will insult and expel him for such a nonsensical application.

The lady must have gone to court to have the registration of the civil „marriage‟ annulled. Such registration is not nikah. The „divorce‟ decree issued by a secular court only cancels the civil registration. This is not kufr.