Legal Question in Landlord & Tenant Law in Illinois

Unfortunately, credit reporting agencies only "report", they make no value judgments or determinations as to the accuracy of the information they've received until confronted with an inaccuracy through an appeal process.

You should ask the building management to send a corrective communication to report the error to ALL of the credit reporting agencies (Trans-Union, Experian & Equifax) AND send you a copy of the corrective communication, which, just because things are the way they are out there in our cyber-world, you should also submit to the credit reporting agencies through their appeal processes or at least contact to make sure the corrective communication was received and that your credit reports and scores have been properly addressed.

If the building management company is willing to compensate you for this effort, so much the better but "innocent" mistakes are generally not compensible. Instead, what you might ask for is a separate letter like a letter of recommendation saying you were a good tenant, paid all your rent on time, left the place in great condition, and that any information to the contrary was an unfortunate error on their part. This could serve you better in the long run.