In Shirley Jackson's "The Possibility of Evil," what is significant about the fact that Miss Strangeworth uses a dull stub of a pencil and childish...

While Miss Strangeworth is viewed as a sweet and elderly woman by the people in her community, she's actually anything but. If anything, Miss Strangeworth is bitter, judgemental, and cowardly. 

She makes polite conversation with her neighbors when she's out and about in town and she always asks questions about how they're doing and what they're up to. 

Her concern appears genuine, at first, but it's soon revealed that Miss Strangeworth frequently writes hurtful letters...

While Miss Strangeworth is viewed as a sweet and elderly woman by the people in her community, she's actually anything but. If anything, Miss Strangeworth is bitter, judgemental, and cowardly. 

She makes polite conversation with her neighbors when she's out and about in town and she always asks questions about how they're doing and what they're up to. 

Her concern appears genuine, at first, but it's soon revealed that Miss Strangeworth frequently writes hurtful letters to her neighbors, most of which are rooted only in gossip.

The narrator describes the locked desk in her house in which she keeps all of her stationary—one "normal" set and a colorful set, commonly used by various townspeople, that she uses to pen her anonymous letters.

It's noted that Miss Strangeworth goes to great lengths in order to keep her identity hidden. She never signs her name on the letters and brings them to the post office only after dusk. 

In addition to that, she always uses the same dull stub of a pencil when writing and she masks her handwriting by making it blocky and childish.

The whittled down pencil stub implies that Miss Strangeworth writes her hateful letters fairly often and the childish handwriting implies that she works very hard to remain undiscovered.

It's also implied that Miss Strangeworth is the one who sent the shocking letter to Linda Stewart's parents, which is why she's no longer allowed to have Dave over to her house.

While the reader is never made aware of the contents of the letter, Linda describes it as being both "dirty" and "nasty."