Is it permissible for the husband, Islamically, to demand the return of the money that the wife's parents took from her dowry without her knowledge, given that the wife does not wish to forgive them for this money?

The mahr (dower) is a right of the woman, and it is not permissible for anyone to take it without her consent, based on the Almighty's saying: "And give women their dowries with good cheer; but if they, of their own accord, remit to you a part thereof, then you are welcome to enjoy it with pleasure and good cheer." (An-Nisa 4:4), and the Prophet's (peace be upon him) saying: "The property of a Muslim is not lawful except with his willing consent."

If the parents take something from their daughter's money without her knowledge, this is forbidden, and they must repent and return the money to her. The wife has the right to demand it. The husband may recover the money if his wife authorizes him to do so; otherwise, he has no right to intervene, to avoid problems between him and her parents.