It seems that Mat was very lucky to survive this encounter at all, because he did not know how to approach them and what bargaining he would need to do. From the way that they responded to his rambling rant, it would appear that they do not answer three questions, as the Aelfinn do, but rather they grant three wishes. Thank goodness he included a wish to return home, otherwise I imagine that they would have decided to remove all of his skin very, very, very slowly. His other two wishes seemed to have been to have his memories repaired and to be immune to Aes Sedai. I cannot see how the medallion would be a way to return his memories, so it seems much more likely that it is a protection of some sort against Aes Sedai or even channeling in general. Of course, this will not stop the Sisters trying to manipulate Mat, but it might make him feel a little more in control of his life.