What is the ruling on the surplus money that the wife received from another party, given that the husband's affiliated party will pay the full amount of the bill? And must she return it or not?

You must inform the entity that paid the increase that your wife has settled the amount. If they permit you to benefit from it, then there is no sin. Otherwise, it must be returned, and it is not permissible to use it before that. A Muslim in those countries is advised to be a good example through his character and his avoidance of bad manners.