…Does the Time Machine go back into the discard pile?

A: To refresh, Engine Trouble states that it can cancel a Time Machine and send the relevant card back to the hand of the player using it.
When someone Rewinds a card, it is as though the card they pulled from the discard had been played from their hand, so, if Engine Trouble is played on a “rewound” Time Machine, it goes back into the player’s hand.