Background misinformation

I did a search for threads on my upcoming question and didn’t find anything related, so...
I have a company that is willing to provide a pre-hire letter, but when running my MVR and background, errant information has come back. The HR person with whom I spoke said that a decision to move forward with a pre-hire letter would be made by her and her boss. Basically, my felony conviction is being noted as a completely different and more severe charge. How can I get this corrected? Without getting it corrected, there is 0 chance for me to be given a chance by a company that isn’t going to take advantage of me.

Side note: This company is a smaller company and not a mega carrier. The HR rep’s boss may likely be the company owner.

 

I sure hope so because otherwise I am wasting my time going to get my CDL

 

I live in Texas and it’s a felony. Suffice to say, Texas is not expunging any felonies, at least not that I’ve heard.
The whole thing is really frustrating because I was talking to a smaller company earlier (Bulkley Trucking) and the HR Rep with whom I spoke, she basically sounded like she was willing to extend a job offer contingent upon me earning my CDL. She said she had to run my MVR and so long as that came back with what I declared, then everything is cool. Well, now I’ve got to wait for her to talk to her boss. I tried explaining how the information she is reading is not accurate, but how can she really take my word for it over her trusted source? Maybe this company will give me a shot anyway.
As far as smaller companies not running backgrounds...Dallas, TX...every company that is worth anything runs a background now. Thank you for the feedback.