the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
The khul` is valid.
Khul` is different than divorce. It can take place during a woman’s menstrual period. When Burayrah appealed to the Prophet (peace be upon him) for khul`, he did not ask her whether or not she was menstruating.
The condition that a man may not divorce his wife during her menstrual cycle is for her benefit, so she will not have a prolonged waiting period (`iddah). Since the khul`is by her request and for her benefit, it does not matter when she requests it.
[Refer to: Ibn Qudâmah, al-Mughnî (10/269)]
Source: Islam Today