First USA Bank They put an unauthorized hard pull credit inquiry on my credit report. Westerville Ohio

I have been working on my credit report so that I may refinance. I have a lot of items that have been removed and updated which should have brought my score up. Not so. First USA Bank, evidently of Westerville, Oh, according to Equifax pulled my credit. I disputed this with Equifax and they say this was a legitimate inquiry. I do not even know who these people are, but they have now negatively impacted my credit report and there is nothing I can do about it right now. I did write the Attorney General of Louisiana in an online complaint. There is no phone number for this company and I really do not want to repeat my social security number these people in a letter. It appears that they are known for doing this. Is this not illegal?

Lindsay
Geismar, Louisiana
U.S.A.