Is it permissible to marry a girl who claims to be able to communicate with and see Muslim jinn, especially since she has agreed not to communicate with them again if they return?

We advise you to perform Istikhara (prayer for guidance) and consult those who know the girl. If she is of good character, there is no harm in marrying her. We also warn that jinn are prone to lying and deception, and a jinn should not be believed except in matters whose truth is known through the Sharia.