From Commentaries On Buddhahood. Lessons on the Writings of Nichiren Daishonin. Letter from Sado. Soka Gakkai Study Dept. Page 33.
By meeting persecution in this lifetime, we can stop the endless downward spiral of negative causation leading us into the hell of incessant suffering. This is why Nichiren calls persecution a blessing.
The perspective of "eradicating karmic offense" is a focus on erasing the influence of negative karma over one's life. Although we cannot actually undo our past in order to make our negative karma disappear, we can eradicate the control it exerts over our lives.
Nam myoho renge kyo
"The present age has developed exactly as the Buddha predicted it would, and Nichiren may be the person of wisdom whom the Buddha described. Though some people wish to help me, either their determination is weak, or, though firmly resolved, they are unable to act on their intentions. Thus, you are one of the very few whose action match their will. You surpass others in your resolve, and it is because of your devoted support that I have been able to survive."
Propagation by the Wise (The Writings of Nichiren Daishonin, page 753)