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Maybe he’s trying to extract more praise out of the item? he’s associated the item with praise and play for sure.
I would think not to implement corrections while the praise article is in his possession (as you may know) unless you want to discourage the behaviour, the behaviour itself was built from something so just rehash the steps and map it out again.
If it was me I would remove said item from his possession on completion of the game and ensure it was never within reach unless I initiated the game.
And as you have stated they can be possessive, so I would make it clear for him when the task is complete. ie “Finish”
My dog Barney brings his food bowl to me once he has finished eating, he will not bring it directly to me when I say “get your bowl” first he needs to parade it around triumphantly, I let him enjoy it… thats “his” reward…its 50/50 he does what I’ve taught him “get your bowl”… he does > praise, he parades it around… he does > self reward, I ask him to “drop” he does… > praise, I say “finished”. task complete. Same thing every time.
