Is money paid to the wife of an influential person capable of redressing injustice considered a bribe, even if the injustice is not redressed, given that it is intended as assistance to him in his capacity as one of those in debt (gharimin)?

There is no harm in giving the debtor what he needs to pay off his debt, seeking the pleasure of Allah; for Allah loves those who do good, and whoever relieves a believer of a distress, Allah will relieve him of a distress on the Day of Resurrection. And the most beloved of people to Allah are those most beneficial to people. Your intention is not flawed by giving the money to the debtor's wife. There is no harm in seeking help to remove injustice from yourself, and this is a good intercession. Paying money to remove injustice is not considered a bribe, even if it is paid to the oppressor himself.