We can infer that Boo Radley both pays attention to and cares about what Jem and Scout do and how they feel.
In chapter 6, Jem, Dill and Scout attempt to make contact with Boo Radley again. They try to reach out to him through the back porch. Unfortunately, they see a shadow and run.
[We] sensed that Jem was not with us. We ran back and found him struggling in the fence, kicking his pants off to get loose. He ran to the oak tree in his shorts. (ch 6)
Nathan Radley has a shotgun, thinking he has seen an intruder. Scout and Jem make up a story about the missing pants, and later Jem goes back to fetch them. He is worried that Atticus will realize that he disobeyed him and be disappointed. When Jem goes back to find the pants, he finds them inexpertly mended.
In chapter 6, we see how Boo Radley is both intuitive and empathetic. He is able to realize that Jem wanted to see him, and also that he would be in trouble for losing his pants. As a result, Boo takes Jem’s pants and mends them. He cares about Jem. He is trying to protect him. Just as Jem and Scout try to protect Boo later in the novel, Boo is reaching out.
As was mentioned in the previous post, the reader can infer that Boo Radley is a sympathetic, caring individual and not the "malevolent phantom" that he is rumored to be. In Chapter 6, Jem is forced to leave his pants behind during the children's raid on the Radley home at night. When he returns to the Radley's yard to retrieve his pants, he finds them sewn and folded on the fence. In Chapter 7, Jem and Scout find several other gifts in the knothole of the Radley tree. These gifts indicate that Boo Radley seeks to become friends with Jem and Scout. Despite his reclusive nature, Boo Radley is watching over the children and offering them his friendship. Jem is old enough to realize that Boo Radley is not the mean-spirited monster that people make him out to be after these several incidents.