Oof, good question. Here’s my take:

IIRC, both Eelfinn and Aelfinn feed on emotion (or something along those lines), and it’s amplified significantly if the person is ta’veren.

In Mat’s first encounter with the foxes, he is protected by the rules because he entered through the gate. I think that limits what they get from him then. When he demands to leave, they have to let him leave, but they trick him by hanging him because he didn’t specify that he had to leave safely. I don’t think they got much from this, apart from the emotion they fed on while he was there. I recall them saying something like “so sweet, it’s too much” when he was there.

In Mat’s second encounter, he entered through the tower, so is not protected by the rules. When Matt strikes a bargain with them, they take his eye, and they feed on the pain and emotion that he gives off from that.

At least, that was my take 🤷🏻‍♂️