Is the money a husband receives as a commission for reducing amounts paid to government entities permissible or impermissible, especially given that the contractor is unaware of the husband's commission percentage?

It is not permissible for a government employee to reduce the amounts owed by a company without the permission of the authorized official. Nor is it permissible for him to accept a payment for this reduction, as it falls under prohibited bribery, and gifts to employees are considered misappropriation. It is also not permissible for your husband to take a commission from the reduction, whether it was rightfully or wrongfully made, except with the permission of the company owner, because he is an agent for him, and whatever he obtains by virtue of the agency belongs to the principal.