We are first introduced to the bullies through one of their hands, or more specifically through Martin's tapping finger.
In the scene where the policeman visits the classroom the film shows us Martin's hand at the edge of frame. One finger is tapping ominously. The film makes sure that we notice it by having Oskar notice it. This is the first hint that the film gives us that all may not be right with Oskar's world.
The tale of Oskar and the bullies is a tale told just by their hands, but by their hands upon him. Conny torments Oskar by pushing his nose to mimic a pig's nose and then by flicking it with his finger. As he does so, the film shows us Conny's hand in preference to showing us Conny's face. It would be easy enough to block this scene out to show Conny's face on one side, Oskar's face on the other and Conny's hand in the middle. Instead the film tells us that Conny the character is not important. By obscuring his face with his hand, the film is letting us know that it doesn't matter who the bully is. This is Oskar's world putting unkind hands on him.
When the bullies accost Oskar after school, once again the film would rather show us a hand rather than a face. Martin and Andreas sneak up behind Oskar and Martin grabs him from behind. The film gives us a shot of Oskar with Martin's hand on his throat. Martin's face however is hidden behind Oskar, although it would have been easy enough to let us see it. What we see once again is a disembodied hand mistreating Oskar.
Although the first scene with Oskar at the pool was already regarding the theme of Oskar & Eli's hands, it was in this scene where that theme crossed paths with the theme of the bully's hand. The scene in fact opens with a shot of Martin's hands in a contemplative pose (if there can be such a thing). The shot then widens to show a similar look on his face. He then goes and engages - or at least attempts to engage - Oskar in a friendly conversation. The film shows us the bully's hands first to remind us that he is a bully. However much he attempts to feign friendship with Oskar, these were the hands that were on Oskar's throat.
And finally come the unkindest hands of all. By whacking Conny, Oskar has gotten rid of Conny as a threat, but it seems that Oskar's world has unending supply of bullies each more cruel than the last. This pair of hands does not intend to just torment Oskar. This pair intends to maim or drown him. The film describes Jimmy's interactions with Oskar almost entirely with shots of his hands.
As the action approaches its climax we are presented with an image of Jimmy's hand on Oskar's head with his fist grasping Oskar's hair, preparing to push him under the surface. This one image symbolizes what Oskar's world had been. Through the bullies' tormenting and the adult's lack of interest, Oskar's world had its hand on his head and it was pushing him under. Oskar was drowning in a sea of cruelty and indifference.
Soon however, as carnage above the surface of the pool ends, we see that Jimmy's arm has been severed. Its grasp on Oskar's head has been released and drifts downward out of the bottom of the frame. By letting Oskar in, Eli has severed his world's hostile grip on him just has she has severed Jimmy's arm. While some viewers have criticized this shot for being a gratuitous bit of gore and also for not making sense in the kinematics of the attack that was taking place out of view, the symbolism of this shot is crucial as the dénouement to the visual theme of the bullies' hands.
Finally we see that not only has Eli stopped the world from holding Oskar under the surface, she is actually uplifting him. The film shows her hand reaching downward from above to raise Oskar to the surface of the pool. She is not only saving him from his previous world, but she is removing him from it entirely.