Miss Strangeworth is primarily characterized indirectly in this short story. This means that Jackson mostly shows us what she is like through her actions and thoughts rather than using an omniscient narrator to tell us what Miss Strangeworth is like.
Because of the indirect characterization, our awareness of who Miss Strangeworth is unfolds slowly. At first, she appears to be a kindly older woman who grows beautiful roses in her yard and is actively engaged in the life of her neighbors. As the story continues, however, we realize that Miss Strangeworth is the author of poison pen letters meant to hurt others in her community.
Miss Strangeworth feels superior to the other people in her town, who don't seem to meet her standards. For example, the librarian can be "sloppy" about her personal appearance, and the grocer is wrong not to instantly remember Miss Strangeworth's order.
As the self-appointed arbiter of good and evil in the town, Miss Strangeworth justifies her letters as a way to keep evil in check. However, she also, we are told, likes writing them.
Miss Strangeworth is a typical woman of her day who has been forced to stuff down her feelings behind a smiling facade of kindness and good will. Because she has never been able to acknowledge her aggressive or unpleasant feelings, as she has been taught they are "bad," they have been bottled up inside her and poisoned her. Now the poison is erupting as she spreads her long repressed malice throughout her community.