My opponent has Captivating Crew in play.
They activate the ability to take control of one of my creatures.
In response I play Perilous Voyage and bounce the Captivating Crew back to their hand.
Do they still gain control of my creature?
Yes, they still gain control of your creature.
112.7a Once activated or triggered, an ability exists on the stack independently of its source. Destruction or removal of the source after that time won't affect the ability.
This is the same for any sort of ability; removing the source does nothing to the ability itself.