You need to consider the way that the mother is presented through what she says and does. In this excellent short story she is initially suspicious of the old man, being distrustful of strange men. However, she, like others (as we find out later), is taken in by his story and believes him. Although she doesn't like to take the umbrella for a price way below what it is worth, and initially just wants to give the old man the money, she in the end accepts the umbrella in exchange for the money and is happy with the trade. As the old man leaves, ironically she talks to her daughter about the importance of judging people correctly, whereas, in fact, she has not done that at all. It is the mother who decides that he is "up to something," which leads them to follow him and discover what his "game" is. At the end of the day, the mother, in spite of her talk of distrusting strange men and being a good judge of character, is just as susceptible to being conned as anyone else, and it is this irony that makes this tale so successful.
mother is suspicious of the old manand feels something fishy about him as he was more polite and courteous. she had some rules or code of conduct for identifying a man.