The battery is held in place by one piece of double-sided tape and has a cardboard piece attached to its top in a same way, probably for additional insulation

Use something plastic to remove the battery, or cut the adhesive using dental floss.

Be careful not to puncture the battery

Battery inside consists of two lithium-ion 3.7v batteries taped together. Overall capacity is 420 mAh or 1.55 Wh, and size is around 10x12x30mm

The battery compartment is slightly bigger than the battery itself, so you may use a new battery of slightly bigger dimensions.