The debacle involving the minister, and then his wife, happens in part IV of the short story "A Rose for Emily" shortly after Emily Grierson meets Homer Barron and starts to show herself around town with him.
Sadly, Homer seems less than respectable to the town, and may be taking advantage of Emily. The townsfolk were basically very concerned to see Emily making a spectacle of herself with a Yankee, of all people. Therefore, they felt that someone had to intervene and make (or try to make) Emily desist this behavior which was affecting her reputation in such a way.
The men did not want to interfere, but at last the ladies forced the Baptist minister--Miss Emily's people were Episcopal-- to call upon her. He would never divulge what happened during that interview, but he refused to go back again. The next Sunday they again drove about the streets, and the following day the minister's wife wrote to Miss Emily's relations in Alabama.
Seriously makes us wonder: What in the world did Emily say to the minister that rendered him unwilling to return to her home? Was he disturbed by her behavior? Was she rude? The fact is that the wife of the minister had to become involved on behalf of her husband to be able to diffuse the situation with Emily and try to mend it.