Does a Shariah-compliant khul' take effect if it occurred at home without witnesses, and the wife was menstruating, knowing that the divorce was not officially registered? Is the wife considered a stranger to me in the eyes of Shariah?

Divorce during menstruation is effective according to the majority of scholars. However, there is no blame upon someone who has been given a fatwa by a trustworthy and knowledgeable person that a bid'i (innovative) divorce does not take effect. As for khul' (divorce at the instance of the wife, with compensation), it is permissible and valid during menstruation, and its validity does not require witnesses or a judge's ruling. Khul' has occurred, and the woman has become irrevocably separated and a stranger [to her ex-husband]. The man cannot take her back except with a new marriage contract, along with the necessity of documenting the khul' in courts to protect rights.