Now, when you've removed those screws, you can easily pop the lid of your puck

There are no latches nor adhesive to hold the lid.

The battery is located on the lid, but the cable is long enough for you to open a puck safely without breaking them.

The battery cable itself has a small white connector.

Disconnect battery cable by holding a puck (side with motherboard) in one hand and pulling white connector using the other hand. No tweezers necessary here, use your fingernails and grab the upper part of a connector, which has small bumps on both left and right side for that purpose.

Do not pull that connector by red and black cables, you may break those

If you can't pull out the battery connector, try doing so again by adding a small left-right shake of your hand when pulling up. This will connector's grip a bit.

Be careful not to bend small pogo-pins in process, those are responsible for delivery power from external magnetic connector to the board, so you could charge the device