Hi,
here are a couple of links which may be of some help.
This link shows how to open an X202e laptop. At 2:26 -2:51 minutes into the video the battery connector is being disconnected. (It does not show the removal of the battery).
https://www.youtube.com/watch?v=Lqx0-g3URiI
This link shows the removal of the battery starting at 3:40 minutes into the video and it is removed by 4:23 minutes.
https://www.youtube.com/watch?v=WxD_zS7p434