Could particles of Comet Wild 2, collected and returned to Earth by the Stardust probe, have been picked up in the outer solar system after the comet formed?

The Stardust probe’s target, Comet Wild 2, is a “fresh comet.” It was perturbed into its present orbit, which takes it into the inner solar system, by a close encounter with Jupiter in 1974. Prior to 1974, calculations indicate, Wild 2 orbited much farther from the Sun. So, Wild 2 has had very little time to accumulate inner-solar-system dust on its surface.