Are there any natural satellites in retrograde Sun orbit? As I watch the video of the asteroids being discovered, all I see is prograde orbits. Their prevalence is fully understandable and justified, but the Sun gets interstellar visitors occasionally and I see no specific reason why it couldn't catch one into a retrograde orbit. They would obviously be a minority and likely not nearly as long-lasting as these in prograde orbits, but they should exist.

Did we observe any? If so, what sort of percentage of the whole are they? If not, why?
Yes, there are, but they are very rare.

Wikipedia has a list of retrograde asteroids, and mentions:


  As of September 2016, of the more than 700,000 minor planets known, there are only 95 known retrograde minor planets.


That means only 0.014% of known minor planets are in a retrograde orbit.

The asteroid with the highest known inclination is 2013 LA2, with an inclination of reportedly (175.189±0.007)° according to the JPL small-body database browser.