Background Check Doesn't Match ROE

I recently accepted an offer with the exception the background checks came back ok. At first they couldn't verify I went to college which I was able to fix simply with a letter from said college. Today I was advised by my potential employer that my last employer put that I was terminated due to behaviour however my Record of Employment states A - Shortage of Work/End of Contract Season. I was able to get EI for the past year but will not get the job if it isn't straightened out. Is the previous employer allowed to do this? Who do I contact if they won't fix it? I'm in NB if that makes a difference.