If an opponent uses Blitzcrank to move my only unit away from a battlefield I control, then I use Ride the Wind during Showdown to move it back, do I score a Conquer point?

Ruling: Yes, you score a Conquer point. You can score Conquer during an opponent's turn as long as you haven't already scored that battlefield this turn.

Sequence:

• Opponent plays Blitzcrank and targets your lone unit at a battlefield you control
• Blitzcrank's ability resolves, moving your unit away
• You lose control of the battlefield (it becomes Uncontrolled during Cleanup)
• Showdown begins
• During Showdown, you play Ride the Wind to move your unit back to the original battlefield
• You gain control and score a Conquer point

Nuances:

• Conquer can be scored once per battlefield per turn, even during an enemy's turn
• The battlefield becomes Uncontrolled after Cleanup when it has no units and is not Contested