Use the spudger tool again and wedge it in between the battery and the housing, pry until the battery starts to separate from the adhesive holding it in place. Once you have the battery disconnected you are ready to replace it.

Despite the fact that the metal spudger is shown being used in this step, make sure to use a plastic opening tool or nylon spudger to pry up the battery. The metal spudger has a much larger chance of puncturing the battery, and thus should not be used.