I have an employer funded retirement HRA which pays for most of my medical premiums. I purchased insurance on an exchange. The exchange sent me a 1095-A form that I entered into turbo tax. Turbo tax then informed me that I was eligible for a tax credit of the full amount. There was nowhere to enter the reimbursement. Since I am not itemizing and pay for my medical expenses with and HSA turbo tax balked at entering the reimbursement in the medical expenses area. So how do I enter the reimbursement in turbo tax?
To quote the IRS: "Unlike HSAs or Archer MSAs, which must be reported on Form 1040 or Form 1040NR, there are no reporting requirements for HRAs on your income tax return." So there won't be anything on your tax return about your HRA, nor anything to enter into TurboTax.
See IRS Publication 969 at https://www.irs.gov/pub/irs-pdf/p969.pdf
In your case, TurboTax will carry the amount of the health insurance premiums over to Schedule A to be a medical expense. As you already seem to know, you should not report medical expenses on Schedule A that were reimbursed another way (like through an HRA).
However, TurboTax actually expects you to enter all medical expenses, reimbursed or not. TurboTax will ask you for the amount of insurance reimbursement and will subtact that from your medical expenses, TurboTax will automatically subtract all HSA distributions, and in your case, on the screen headed "Tell us about anything received in medical reimbursements", add the HRA amounts that went to the health insurance premiums here.
Now, if it turns out that TurboTax will not choose Itemized Deductions for you anyway because they aren't larger then the Standard Deduction, then do nothing, because the HRA payments won't make any difference anyway.