What are the words a husband must ask to know whether his divorce is irrevocable or revocable? And is the husband's internal consent to the wife waiving her rights sufficient for the divorce to become irrevocable, or is verbal consent required?

It appears that what transpired between the spouses was not a khul‘ (divorce at the wife's instance with compensation), due to the absence of the formula of offer and acceptance for khul‘. The wife informed him that she did not want any right from him after the divorce, so he divorced her without any condition. Therefore, if this divorce does not complete the three divorces, it is a revocable divorce (ṭalāq raj‘ī) and not an irrevocable one (bā’in); because the default rule for divorce is that it is revocable. It is advised to present the matter to scholars so they can inquire further from the husband and issue a fatwa (definition) based on that.