Can an injustice be rectified by saying, "Forgive me for everything," after backbiting or insulting, and will Allah forgive the oppressor if the wronged person refuses to forgive, even after the oppressor has done what is required?

Oppression, backbiting, and insulting are grave prohibitions. The perpetrator must offer sincere repentance and seek forgiveness from the one they wronged, because the rights of people are based on strictness (mushahah), and Allah does not forgive them except with the pardon of the rights-holder. As it is established from the Prophet, peace and blessings be upon him, Allah will not leave anything of people's rights on the Day of Judgment.

It is better for the oppressed to forgive in order to attain reward and recompense. If the oppressed refuses, then the oppressor should increase in supererogatory acts and good deeds, supplicate for the one they wronged with goodness, and mention their virtues in the gatherings where they backbit them.