Is the money paid to a real estate agency to obtain housing in this manner considered a bribe, and what is the path to repentance if the housing has been utilized?

It was previously explained that bribery is one of the major sins if it is for nullifying a right or establishing falsehood. However, it is permissible to pay it to achieve a right or ward off injustice, and the sin falls upon the recipient of the bribe, not the briber. If the money paid is part of the price or to have your name included among those who are eligible, and you are indeed eligible, then there is no blame upon you. But if the money is intended to influence officials to favor you despite your not meeting the conditions, then it is a forbidden bribe. In this case, the housing unit must be returned to the relevant authority, and the briber should seek to recover the money paid from the recipient of the bribe.