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.