How should one act concerning the threat from the husband of a woman with whom an illicit relationship occurred in the past, knowing that I have repented and regretted my action, and I fear scandal and legal repercussions?

You have done well by repenting to Allah for adultery, especially since it was with a married woman. Let your repentance be sincere and fulfill all its conditions. Strive to ease your burden, and remember that no sin is too great for Allah's mercy and forgiveness. Increase your seeking of forgiveness and ask Allah for concealment in this world and the Hereafter. You must conceal yourself and not confess to adultery, for the Prophet, peace and blessings be upon him, said: "Whoever is afflicted with any of these abominations, let him conceal himself with Allah's concealment." As for the woman's husband, if you can improve your relationship with him and then implicitly seek his forgiveness without causing mischief, then do so. Otherwise, seek forgiveness for him, supplicate for him, and increase in good deeds. Al-Ghazali said that explicit seeking of forgiveness might lead to discord and anger, and it is better to turn to Allah so that He may be pleased with you.