If they will not correct this, you would have to file substitute a Form 1099-R (Form 4852) showing the distribution as an ordinary distribution instead of a return of excess contribution. This form has an area to supply and explanation.
Separately, you could potentially get the distributed amount into a traditional IRA by doing a late rollover under IRS Rev. Proc. 2020-46. However, the circumstances don't exactly correspond to any of the listed reasons for missing the 60-day rollover deadline. Financial-institution error would be the closest acceptable reason, but the employer who made the error is not really a financial institution.
I imagine that correcting the error would be the responsibility of the entity that issued the Form 1099-R, that being the plan administrator. For the plan administrator to do their job at all, the plan administrator needs to know the amount of the employee's compensation and likely should be the entity determining the employee's status as an HCE.
