Is seeing private pictures that show something of a girl's 'awrah, without her knowledge, an injustice that necessitates seeking absolution from her, or is repentance sufficient after feeling remorse, knowing that no one is aware of the matter except Allah?

You have sinned by looking at the picture of the woman whose awrah was exposed, due to the incitement to fitna it contains. You must repent to Allah Almighty. This girl has no right over you that necessitates seeking her forgiveness, because the fundamental principle is the blamelessness of one's conscience.