Are the funds that a father receives in exchange for changes in building specifications, such as reducing the thickness of rebar, permissible or forbidden?

It is forbidden to help contractors violate building conditions and specifications, and the money taken for doing so is unlawful (haram); due to the Almighty’s saying: "And do not cooperate in sin and aggression" and "O you who have believed, fulfill [all] contracts." If your father is responsible for supervision, then his action involves a betrayal of trust and bribery.