The use of this word might cause readers to believe that Gurov has formed a negative impression of Anna Sergeyevna. However, Gurov is actually suggesting that despite her youth and laughter, she is somehow unhappy.
Literally translated from the Russian, this means "she never used the 'hard sign' in letters." The hard sign (ъ) is a feature of the Russian alphabet. This was characteristic of a progressive intellectual at the time and anticipated the reform of the Russian alphabet.
At this point, the dog has been referred to as a pet dog, a little dog, and now, simply, the dog. The original Russian uses the word собачка (sobachka), which is a diminutive form of the standard word for dog. The dog's role is the story is limited and primarily serves as a way for Gurov to use it to his own advantage in order to introduce himself to the lady.
This translation is a little misleading since Gurov hasn't met the lady yet. Instead, the original Russian word встречал (vstrechal) has a connotation of encountering someone without actually interacting with them.