The pebble was "e-paper" which was a marketing term for a transflective LCD. It was not e-ink.
E-ink is a proprietary display tech that uses actual magnetized "ink" suspended in "liquid" cells. By pushing and pulling dark/light ink particles with an array of tiny electromagnets, it physically "paints" an image onto the display surface. Even if you entirely cut power, the image remains indefinitely.
Transflective LCD, is an LCD, and while its an extremely small amount, it does still need power to stay on.