Push the tip of a spudger beneath the rubber adhesive and toward the battery to free it from the surface of the logic board.

Start freeing the adhesive from around one of the outer leads, then free it from the two gaps between leads, and finally push the spudger along the back side of the leads to completely remove it from the logic board/battery leads.

The battery leads are delicate, so be careful to not tear them while removing the black adhesive.