If you are in Sichuan province already, you can contact the provincial foreign affairs department; they have influence on both schools.

If you are changing provinces, you need to contact your current province foreign affairs department. Be sure to provide them with the contact information for BOTH schools. Let your current school know that you are doing this.

There is a distinct possibility that you do not know the entire story: there may be a reason that BOTH schools are attempting to step back from their contractual agreements and this 'fee dispute' is the contrived means to do so. Schools in China are notorious for finding 'medical' or 'regulatory' reasons to end a FT's employment and will go to great lengths to avoid disclosing the genuine reason.

If the 'fee' is genuine, find out how much it is. It may be simpler to just absorb the cost yourself.