It is necessary that two Muslim witnesses are available at the time of ijab-o-qubul (exchange of proper words of nikah) for nikah to be valid, and apparently in the question mentioned above there is no witness available. If it is so that no witness was available at the time of ijab-o-qubul then this nikah was not valid as per the Shariah. Hence both the boy and girl may move out of this relationship without talaq or khula rather it is haram for them to meet each other.
Allah knows Best!
Darul Uloom Deoband