Answer:
Jem does not want Atticus to return the blanket so as not to cause problems for Boo.
Step-by-step explanation:
If Atticus returned the blanket to the family, then Mr. Radley would know that Boo had left to give him the blanket and that would cause her many problems.
Jem doesn't want Boo to be reprimanded for having brought a blanket to warm Scout.
He realizes that Nathan doesn't want Boo to have contact with them because the knothole of the tree was covered with cement.
Finally Atticus says that he will keep the blanket.