This will all happen automatically in Turbotax, and it gets reported on form 8889. The one thing you may need to verify is that the removal of the excess funds was coded by the HSA bank as a "removal of excess funds" and not a regular withdrawal. Also, you must withdraw any earnings on the excess contribution (this might be a small amount of interest, or maybe nothing if the issue was discovered immediately.)
Turbotax will "see" the contribution from the employer on your W-2. That will cause the program to ask you about your insurance coverage. When you answer that you did NOT have a qualifying HDHP, the program will tell you that you need to remove the excess or pay a penalty. You can answer that you already removed or will remove the excess. That will cause the program to add the amount to your taxable income. Tuurbotax should also ask about any earnings, they are also taxable.
You will also get a 1099-SA from the HSA plan at the end of January, this is a statement of your distributions. The statement should have code 2 for withdrawal of excess contributions, and not code 1 for a regular distribution. You must enter this in Turbotax as well. The withdrawal won't be taxable again (because of code 2), but it needs to be there to satisfy the IRS. If the 1099-SA shows code 1, you will need to get it corrected, which is why you may want to double check (unless you already confirmed) that the withdrawal was a "withdrawal of excess" and not a regular withdrawal.
