Eclipses of Jupiter's Moon during Retrograde motion
The fact that eclipses are either "early", "on time" or "late" only depend on the distance between Jupiter and the Earth. Since the speed of light is not infinite, a longer distance means a longer delay between the actual eclipse and the time it is observed from Earth.

For superior planets, retrograde motion occurs around opposition, at a time when the distance between the planet and the Earth is minimal. So you should expect eclipses to appear early during retrograde motion. But note that the early eclipses are not a consequence of retrograde motion: they are both consequences of keplerian motion.