Is interceding to be discharged from the army unlawful if the person is medically unfit, and is that considered a blameworthy intercession?

If the system exempts you from military service, then it is permissible to seek the help of someone who can facilitate your exemption. If this requires paying money to an intermediary, then there is a detailed explanation: it is permissible for the intermediary to take money if their work is not related to determining who is exempt from military service. Otherwise, it is not permissible for them, as it would be considered a bribe. It is permissible for you to pay the money if you cannot obtain your right otherwise, and the sin falls only upon the recipient if it is a forbidden bribe.