Is a separation considered Khulʿ or divorce if the husband requests Khulʿ from his wife after she has requested a divorce, and he agrees to release her without financial compensation, and this occurred during a period of purity in which he had intercourse with her?

A man's statement to his wife: "I agree to release you" – if he intends thereby mere agreement to separation without initiating divorce, then nothing occurs. However, if he intends thereby to initiate separation, then it constitutes a revocable divorce (ṭalāq rajʿī) and not a khulʿ (divorce at the wife's instance, often for compensation). Khulʿ requires offer and acceptance, and if the wife does not agree to it, it does not become khulʿ, but rather a divorce. If this divorce occurs after the wife has been intimate with him during her period of purity, it is a forbidden, innovative divorce (ṭalāq bidʿī), and the preponderant juristic opinion is that it does not take effect.