If it is my turn and I charm an opponent's unit from a battlefield they control to another battlefield and let it resolve, then they play Thrill of the Hunt to move their unit back to the original battlefield, will they score a point?

To determine if your opponent scores a point in this scenario, we must look at the rules for Conquering and Scoring.

The Ruling

Yes, your opponent will score a point if they move their unit back to the original battlefield and win the resulting showdown, provided they have not already scored that specific battlefield this turn.

Sequence of Events

1. Your Turn: You play Charm to move your opponent's unit from their battlefield (Battlefield A) to another battlefield (Battlefield B).
2. Resolution: The unit moves to Battlefield B. Because this move causes Battlefield B to become contested (assuming it was not already controlled by your opponent), a showdown occurs at Battlefield B.
3. Opponent's Reaction: Your opponent plays Thrill of the Hunt in response to the situation or during the open state following the resolution of Charm.
   • Note: Thrill of the Hunt banishes the unit and then allows the owner to play it to any battlefield.
4. Moving Back: Your opponent plays their unit back to their original battlefield (Battlefield A).
5. Scoring:
   • When the unit arrives at Battlefield A, if that battlefield was not already controlled by your opponent (e.g., if your Charm action caused them to lose control of it), the battlefield becomes contested.
   • If your opponent wins the showdown at Battlefield A, they Conquer the battlefield.
   • According to Rule 464.1, a player scores by gaining control of a battlefield they did not yet score this turn. As long as they have not already scored Battlefield A this turn, they will gain a point.

Key Nuances

• Scoring Limit: Per Rule 465, a player may only score each battlefield once per turn. If they had already scored Battlefield A earlier in the turn, they cannot score it again, even if they move a unit back to it.
• Conquer vs. Hold: The point gained here is a Conquer point. If this is the final point needed to win the game, remember that in standard 1v1 play, you must have scored every battlefield this turn to gain the winning point via Conquer (Rule 466.1.b.2).
• Control: Per Rule 187.4, control is established by having units at a battlefield after a showdown. By using Thrill of the Hunt to return their unit to Battlefield A, they are effectively re-contesting and re-establishing control, which triggers the opportunity to score.

This is my interpretation based on the rules for Scoring (Rule 462-466) and Control (Rule 187). No official FAQ exists for this exact combination of Charm and Thrill of the Hunt, but the mechanics follow the standard rules for battlefield control and scoring.