Jem does not want Atticus to return the blanket to Boo, because he does not want to get Boo into trouble.
After Miss Maudie’s fire, Atticus realizes that Scout has a blanket on her shoulders. She swears to him that she has no idea where it came from, and the Jem remembers that Nathan Radley was at the fire.
Jem tells Atticus about the treasures left in the tree, and Nathan Radley’s cementing the hole.
“…Mr. Nathan put cement in that tree, Atticus, an‘ he did it to stop us findin’ things—he’s crazy, I reckon, like they say, but Atticus, I swear to God he ain’t ever harmed us, he ain’t ever hurt us, he coulda cut my throat from ear to ear that night but he tried to mend my pants instead… he ain’t ever hurt us, Atticus—” (chapter 8)
Jem is worried that Nathan Radley will be angry at Boo for leaving the house and going near the children. Atticus understands, and agrees not to return the blanket.
This incident once again demonstrates Boo's true character. Jem is starting to realize that Boo is a decent man, just reclusive. He also understands that Nathan Radley’s cruelty to Boo is one of the causes of his strangeness.
As was mentioned in the previous post, Jem does not want Boo's older brother reprimanding him for leaving the home to warm Scout. Jem understands that Nathan purposely does not want Boo to have contact with them which is why he covered the knothole of the tree with cement. Nathan Radley is similar to his father in the way that he oppresses Boo. If Atticus were to return the blanket to Boo Radley, Nathan would surely find out that Boo is still in contact with the children. Nathan forbids his brother from leaving the home and is against Boo forming any type of relationship with the Finch children. Jem feels that Nathan Radley is crazy and fears for Boo's safety. Fortunately, Atticus calms Jem down and agrees to keep the blanket for the time being.