The title refers to the possibility of evil occurring in Miss Strangeworth's town. At the start of the story, the name of the protagonist immediately gives one pause. We are led to question why the author gives her such a surname.
As the story progresses, this becomes clear in the way Miss Strangeworth sees herself. She fancies herself the mother of all good intentions and the self-imposed defender of moral values in her small town. Alas, we are led to question the 'strange' value she places on her own 'worth': the author tells us that Miss Strangeworth is not a woman concerned with facts. All the letters she writes to the unsuspecting victims of her twisted ministry are steeped 'in the more negotiable stuff of suspicion.'
In the story, Miss Strangeworth sees herself as a sort of herald who warns others of 'possible evil lurking nearby.' She fancies herself unique in her mission. After all, there were 'so many wicked people in the world and only one Strangeworth left in town.' It never occurs to Miss Strangeworth that her 'strange' way of helping her town and justifying her own 'worth' may actually be harmful to her fellow citizens.
Jackson explains the meaning of her title by highlighting Miss Strangeworth's strange preoccupation with the possibility of evil. Her rich use of imagery and symbolism (through the roses) supports a fascinating short story about the delusions of a self-imposed guardian of morality.