Is it permissible to give the housemaid $100 instead of the $125 agreed upon with the recruitment office, given that the housemaid is content and unaware of the original salary?

It is not permissible to violate the agreement between you and the agency regarding the maid's salary, because the agency acts as her representative, and violating an agreement is not permissible, as the Prophet (peace and blessings be upon him) said: "Muslims are bound by their conditions in what is lawful."