Pearl seems to think, on some level, that Roger Chillingworth is the Devil, whom she calls "the Black Man." In her childish innocence, she certainly picks up on the truth that Chillingworth is diabolical and that there is some link between him, Reverend Dimmesdale, and her mother, Hester.
In Chapter 10, Pearl says,
"Come away, mother! Come away, or yonder old Black Man will catch you! He hath got hold of the minister already. Come away, mother, or he will catch you! But he cannot catch little Pearl!"
With a child's perception (and children are very often able to see things that adults miss), Pearl understands that Reverend Dimmesdale is now at the mercy of Chillingworth; that the Devil, indeed, has captured him. Surely, the fact that Dimmesdale sinned by sleeping with Hester and now sins further by adding deception to his lie of omission (failing to confess), could be read as the Devil having caught him. Now, Chillingworth exploits Dimmesdale's guilt in order to torture Dimmesdale for sleeping with his wife.
Pearl also perceives that the Devil has not caught her mother yet, but she is also aware of Hester's scarlet letter and the fact that Dimmesdale always keeps his hand over his heart. She has linked these two symbols together in her mind: a link which is extremely appropriate because the same initial sin unites them; however, Hester's torment is external, as the letter, and Dimmesdale's is internal, secreted away within him. Hester's public atonement for her sin seems to keep her out of the Devil's clutches, but still connected to him through Dimmesdale.
Pearl, however, is innocent of sin, so there is no way for the Black Man to catch her. She is immune to him in a way that neither her mother nor Dimmesdale can ever be, as long as Dimmesdale's role as Pearl's father remains a secret. Although I could not find a direct reference to Chillingworth's inability to smile or nod at Pearl, it seems very likely that this would be an extension of his lack of ability to control or affect her because he has no knowledge of any sins of her own with which to do so.