I believe that the only interaction that Miyax has with the wolves involving a mitten occurs with Kapu, not Amaroq.  That incident happens when Kapu is still a pup.  Wanting to play, Kapu nips Miyax' heel softly, and she, recognizing his request for attention, pulls a mitten from her pocket.  Before she even has a chance to shake it in front of his nose, Kapu leaps and grabs one end of it, "pulling and shaking (Miyax') whole arm and torso with incredible strength".  Miyax is forced to let go, and Kapu, who had been tugging with all his might, rolls "head over heels into the lichens".  Recovering himself, Kapu takes a firm grip on the mitten and dashes down the slope and into his den.  Once there, he looks back to see if Miyax is following.

Miyax calls to Kapu to bring back the mitten, telling him that she needs it, but Kapu, flashing a "wolf smile of apology", shakes the mitten and proudly romps with it amidst the other young wolf pups.  He marks the ground deeply with his hind legs, showing off his prize to the others with a playful arrogance which is humorous to watch (Part 1 - "Amaroq, the Wolf").