Ultimately you need to deal with Apple about this if not satisfied. Nobody here in these volunteer user forums can help with this. If the battery had swollen, the store would be able to determine that. But in the absence of any discernible defect or malfunction, the fault for damage tends to fall on the owner.
From your photo, quite honestly it looks to me like it got bent while pressed up against something? Accidental or otherwise, that would qualify as non-warranty accidental damage. It's hard to imagine a swollen battery bending it in the middle like that - swollen batteries usually manifest themselves by pushing the screen and bezel apart from the frame, and bulging out the back of the device.