When you draw the Mythos Headline Goat-like Creature Spotted in Woods! any Dark Young in Arkham are returned to the cup.

What happens if the Mythos card The Terrible Experiment is in play & there is a Dark Young on the card, do you leave it there or do you return it to the cup.

The Monsters on the Terrible Experiment are not considered "In Arkham;" they are just "In Play." So the Dark Young on the Terrible Experiment remain.

From the Terrible Experiment card: "These monsters do not move, are not considered to be on the board, and do not count against the monster limit."

So I would assume the card wouldn't effect any monsters that were part of it since they aren't in Arkham.