Jem's memories of the time when Atticus, his father, defended Tom Robinson unfortunately include Jem's broken arm. Bob Ewell broke Jem's arm in an attack on Atticus's children in retaliation for Atticus's defense of Tom Robinson. Therefore, Jem's memory box might include the cast he wore after Bob Ewell's attack. He might also include the ham costume that Scout wore to the Halloween pageant on the day Bob Ewell attacked them.
Jem would also include the items that Boo Radley left for him and Scout in the knothole in the tree, including sticks of gum, coins, twine, soap figures that look like Jem and Scout, an old watch, spelling bee medals, and a knife. Finally, Jem might put into the box the air rifle and chemistry set that he received for Christmas. Atticus advises Jem to shoot cans in the backer. If Jem insists on going after birds with his new rifle, Atticus tells him only to shoot bluejays, not mockingbirds, because mockingbirds are defenseless creatures. This is essentially the lesson of the book--not to injure creatures or people who have no means to protect themselves.