You may find that a letter on your attorney's letterhead will suffice to encourage the former employer to correct their records.

I once had an a former employer report that they wouldn't hire me again. When I learned of it, I called the former employer to ask why they made that statement. The flight department had closed, and they wouldn't be hiring any pilots again, as the aircraft was sold. I explained that their answer would cost me a job, so they contacted my prospective employer and corrected the error.

If the former employer won't work with you or correct the problem, your best recourse is to make this information known to your prospective employer.

If former training records contain inaccurate or incorrect information, the FAA may be interested; those records are required documentation. If the records are falsified to the point of stating that you failed a checkride, for example, then paperwork will need to reflect that, and if that's falsified, the former employer has a big problem. In such a case, the FAA may be your friend (much as it pains me to say that).