Is there any religious basis for stipulating forgiveness in exchange for money or anything else, or is simple forgiveness sufficient without conditions?

Forgiving the oppressor is commendable in Islam, as Allah and His Messenger have encouraged it, as stated in His saying, the Almighty: (So whoever pardons and makes reconciliation - his reward is due from Allah) and His saying: (But whoever is patient and forgives - indeed, that is of the matters [requiring] determination), and the saying of the Prophet, peace and blessings be upon him: "Allah increases a servant in nothing by forgiveness except honor." Forgiveness does not require paying money unless the injustice was financial, or if the wronged person stipulated that for his satisfaction. Paying money is better than having the injustice settled from one's good deeds on the Day of Judgment.