Alright, so it turns out the parents' plan is not an HDHP but a POP. So it looks like I was not eligible to contribute to an HSA last year (2016). With this being the case, do I need to close the HSA entirely, or just remove funds that I contributed last year? I plan on getting off of my parents' plan this year (2017), so would like to keep the HSA contributions from this year, if possible.

The limitation is month-by-month, so if you are still under that plan now, you can't contribute to the HSA until the month in which you were free of the non-HDHP policy on the first day of the month. Get off of that PPO plan now.

Immediately contact your HSA plan administrator and see if they will give you a form for "Mistaken Contribution". There will probably be different forms for 2016 and 2017. You want to withdraw all of the amounts contributed during any month in which you under the non-HDHP plan.

You will have to report these contributions as income in both years. Perhaps the easiest way is to tell TurboTax that you were not covered by an HDHP when it asks. This will cause all contributions to be excess contributions.

Then TurboTax will ask if you will withdraw all of these contributions by April 18, 2017 (so you need to get right on this). If you answer "yes", then TurboTax will add the HSA contributions back to line 21 on the 1040 as Other Income. Now your tax will be correct.

If your HSA won't do the Mistaken Contribution form (I am not sure that they are required to), then tell them that you want to withdraw an excess contribution - make sure they hear that or else they might think that it's a normal distribution. Make sure they know it's for 2016.

If you made any contributions in 2017 while under that other plan, you might as well start the same process.