What is the ruling of Islamic law concerning a man who divorced his wife with a single pronouncement and then took her back after her 'iddah period ended, without her knowledge?

If a man divorces his wife with the first or second pronouncement, he has the right to take her back during her 'iddah (waiting period) without the need for witnesses. Witnessing is recommended but not obligatory according to the majority of scholars. If the 'iddah ends, she does not become lawful for him again except with a new marriage contract and a new dowry. However, if it was the third pronouncement of divorce, she does not become lawful for him until she marries another man.

If the husband claims he took his wife back after the 'iddah has expired, and the woman denies it, her word is accepted according to the majority of scholars, unless the husband provides evidence that he took her back during the 'iddah, in which case the revocation is valid. Some scholars are of the opinion that the husband's word is accepted if he claims to have taken her back during the 'iddah and the woman denies it.