Is it permissible for a wife to return to her husband with a new contract after being divorced by him twice, and then seeking a Khul' (dissolution of marriage) through a court order without his consent or knowledge?

Scholars have differed on the ruling concerning khul‘ (divorce at the instance of the wife): is it a talaq (repudiation) or a faskh (annulment)? If it is an annulment, then it is permissible to return to the marriage with a new contract. If it is a talaq, then the husband does not have the right to return to his wife unless she marries another man willingly and he consummates the marriage with her, and then he divorces her or dies, and her waiting period (iddah) from him ends. If the khul‘ is issued by the court without the husband's knowledge, he must review the court to correct the procedures.