If you did not have HDHP coverage at any point in 2017, then, as you know, you are not eligible to have any contributions made to your HSA. What your company is doing is creating a lot of unnecessary work for you, your tax preparer, and the IRS. I can't imagine that the IRS would be amused to find the company doing this as a matter of policy.
How should they handle it? If they wanted to give you some money for medical expenses that matches what they are doing for HSA owners, then they should put the amount in box 14 with some code like "MedMatch" - they can make up whatever they want, because box 14 entries are not defined by the IRS.
The box 14 entry should be included in your Wages in box 1, making it after-tax. The box 14 entry will not trigger any special processing by TurboTax, so no unnecessary 8889(s) and no error messages.
You might show this post to HR to see if you can spark a positive reaction. Also note that if payroll took the code W amount out of Wages in boxes 1, 3, and 5, well, the excess contribution that we are going to force will take care of Wages in Box 1 (because they are being added back to line 21 (Other Income)), but your employer is incorrectly underwithholding your Social Security and Medicare taxes - and you are liable for them if the IRS ever catches it. (No, you can't fix it on your income tax return).
You really need to bring this up with your HR/payroll department.
As for what you need to do:
1. When you see the question, "Was [name] covered by a High Deductible Health Plan (HDHP) in 2017?", check "I had coverage at least one month out of the year.".
2. When the three new lines appear below, then check "I had different types of coverage at different times of the year".
3. On the next screen, mark each month as "None".
4. Yes, you could have marked "No" on the previous screen, but I am hoping to reduce the number of messages you have to fix.
5. When you go through the Federal Review, I think you will get an error message like this:
Check this entry
Form 8889-T: HDHP coverage check box needs to be checked to indicate the type of coverage held under a high-deductible plan during 2017.
No entry
Line 1, Self
Line 1, Family
6. You can answer either Self or Family (it doesn't matter because you have already marked None for each month, but answering Self or Family will let you e-file).
Continue with your return.
