Does my opponent's weapon get returned if I play Thrill of the Hunt on Akshan?

To answer your question: No, your opponent's gear is not returned to them just because you used Thrill of the Hunt on your Akshan.

Here is the breakdown of why this interaction happens this way:

1. Thrill of the Hunt's Effect: When you use Thrill of the Hunt to banish your Akshan and play him again, you are effectively "resetting" that specific Akshan unit.
2. Akshan's Control Effect: The control-change effect created by Akshan states that you control the stolen gear "until I leave the board." When you banish your Akshan via Thrill of the Hunt, he leaves the board, and the control-change effect he created ceases to apply.
3. Recalculation: Because your control-change effect has ended, the game recalculates control of the gear. If there are no other active control-change effects affecting that gear (e.g., if you haven't stolen it with another card), control of the gear will revert to its original owner.
4. Important Nuance: As established in RiftJudge FAQ #9043 and #10186, while you lose control and the gear reverts to your opponent, the gear does not automatically detach or return to their base. It remains attached to whichever unit it was currently on.

While you no longer control the gear and cannot use its activated abilities, it stays on the board attached to its current unit until your opponent moves it or the unit it is attached to leaves the battlefield.

This is my interpretation based on the rules for control-change effects and the precedents established in RiftJudge FAQs #9043 and #10186. No official FAQ exists for this specific interaction with Thrill of the Hunt.