The Widow Douglas had been married to Judge Douglas while he was still alive and active. As the judge in the town court, he had been involved with Injun Joe on numerous occasions over the years when Injun Joe had been arrested and brought before the court for one offense or another. He doesn't have any particular grievance with the Widow herself, but has great reason, in his perception, to be upset with the Judge. Injun Joe plans to take revenge on the widow because the Judge is no longer alive and able to pay for his insults to Joe's person and character.
He had me horsewhipped!-horsewhipped in front of the jail, like a nigger!-with all the town looking on! HORSEWHIPPED!-do you understand? He took advantage of me and died. But I'll take it out of her.