How sincerely concerned are the townspeople of Salem for the souls of Hester & Pearl?
The settlement's sentiment towards everything is meant to be hypocritical and to hold double standards. All through the novel we see how the elders rule while one of their own impregnated a woman and left her to her disgrace. We see how they all cry "witch" while allowing a self-confessed witch and necromancer live among them in an even better status than Hester. In all, the entire town is allegorical of how the sins of the people require a scapegoat so that society can feel better about itself.
Nobody cared about Hester and Pearl- all they needed was a pariah, or scapegoat that they can blame, use as an example, talk bad about, and feel better about themselves. Hester was the topic of sermons, and the emotional punching bag of a town full of hypocrite puritans. Therefore, there is no sincerity in the hearts of any of the people in Boston.
If anything, at some point in the novel it seemed as if Hester had become a soldiering member of society, Scarlet letter and all, but we come to find out that Hester was as fed up with her people towards the end as they had been angry at her.