Unsolder the red and black wire from th logic board.

Here is the reason for loosening the logic board. Push it lightly below the level of the battery.

Shimmy the battery toward the logic board. It will just clear the back of the housing.

Angle the battery to one side to remove it from the housing. The plastic of the housing, as well as the battery have a very small amount of flex. This flex is enough to free the battery.