The roses symbolize Miss Strangeworth's sense of privilege and pride. Because they were planted by her grandmother, they represent a kind of inheritance, in the same way she feels ownership over the town itself, which, she thinks, would not be here were it not for her grandfather. This sense of ownership translates into a feeling of responsibility for emotional and moral health of everyone in the town. In this regard, they also symbolize her sense of superiority to other people.
Several details suggest Miss Strangeworth's fixation on the roses as a kind of emblem of her status within the town. For instance, she never allows anyone to take any roses. When they are cut, their use is reserved exclusively for her own house. In fact, there is a kind of fairy-tale quality to her house, which seems like a place out of time, filled with furniture and decorations left by her mother and grandmother. The roses and their scent mark the place as "home." In a way, like in a fairy tale, the roses seem to have an almost magical quality, as if it is the roses which account for Miss Strangeworth's place in the town.
In that sense, the roses function ironically. On the one hand, they are beautiful and have a lovely scent; on the other, as a symbol of pride, they represent the ugliness of Miss Strangeworth's letters, which spread fear and misery throughout the town. When her identity as the letter writer is found out, and her roses are destroyed in retaliation, it is as if the secret, evil nature of the roses has been uncovered. The moral rectitude Miss Strangeworth values so much finds expression in the destruction of the very thing that represents her identity.