Is the khulʿ considered valid if it was done without witnesses and without returning the dowry to the husband after he waived it?

Scholars have differed on the validity of khulʿ (divorce at the wife's instance) without compensation. Many of them held that it is not valid, while others, including Shaykh al-Islam Ibn Taymiyyah, maintained its validity. They argued that the right of rajʿah (reconciliation/revocation of divorce) is a right of both spouses, and waiving it by mutual consent is permissible. Alternatively, khulʿ without compensation is considered compensation by virtue of the wife forfeiting her right to maintenance and housing, and the husband forfeiting his right to rajʿah. It is safer for the wife to redeem herself from her husband with something, even if slight, or by waiving her deferred dowry, in order to avoid disagreement. Witnessing the khulʿ is not obligatory.