Is there a planet or planetary moon flyby path that could send a solar prograde orbiting asteroid into a retrograde solar orbit?
If an asteroid on an inner orbit catches up with a planet on an outer orbit, and passes close enough to the planet to be strongly influenced by the planet's gravity, it can whip around the planet ahead of the planet and then move in and orbit backwards (retrograde) farther from the sun than the planet.
So the asteroid might be captured by the planet if its retrograde speed is slow enough, and then move in a backwards or retrograde orbit around the planet. A lot of small asteroid sized moons of the giant planets have retrograde orbits indicating they were captured that way - also Triton, the large moon of Neptune. I just counted abut 119 natural satelelites with retrograde orbits in our solar system.
And the the asteroid's retrograde speed after passing around the planet is fast enough, it won't be captured by the planet but will continue to orbit the Sun, but in a retrograde orbit.
In fact, a very tiny percentage of all known asteroids have retrograde orbits, only 82 out of more than 726,000.