The town thinks Miss Emily's "two female cousins are even more Grierson than Miss Emily had ever been" (4.4). That is definitely not a compliment. These cousins from Alabama are relatives of old lady Wyatt and had been estranged from Emily's father since the time of old lady Wyatt's death. In fact, they were so estranged that they didn't even show up to Emily's father's funeral.
The situation with the cousins exposes some of the dark irony of the story. The townspeople call in the cousins to stop Emily from dating Homer, but when they decide they hate the cousins, they switch sides and try to push Emily and Homer together.