Miss Strangeworth sees the town as her town. Her grandfather built the first house on Pleasant Street, as she proudly tells tourists, and this gives her a sense of proprietorship over those who live in the town. As such, Adela feels entitled to wear the mantle of local moral guardian, which involves doing all she can to root out the least sign of what she regards as immorality.
That's why she writes poison pen letters to various people in the town. Although the letters are thoroughly nasty and detestable, Miss Strangeworth genuinely thinks it's necessary for her to write them in order to maintain a high moral climate in town. The irony here is inescapable; Miss Strangeworth engages in immoral actions for the good of morality.
This bizarre and delusional attitude ultimately stems from what we saw earlier: Miss Strangeworth's proprietorial attitude to the town and its inhabitants. So long as the old lady genuinely thinks that this is her town and that she therefore has the right to act as the guardian of its moral climate, then she will continue to write such horrible letters.
Even when Adela gets a taste of her own medicine, she shows no regret for her actions. Instead, she cries silently for the wickedness of the world. In other words, she's not wicked; other people are. In her own mind, at least, she's still the paragon of virtue.