The explanation that you received with the check indicates that the $166,66 was not included on the Form 5498-SA, so I based my reply on that. Had they deposited the $166.66 into the HSA in February 2016, it would have been included in box 2 of the 2016 Form 5498-SA. If the deposit was supposed to be part of your 2015 HSA contribution, it would also have been reflected in box 3 of your 2015 Form 5498-SA.
To really understand what contributions were reported as contributions for 2016, you need your 2015 and 2016 Forms 5498-SA. The amount contributed for 2016 is the sum of the amounts in boxes 2 and 3 of the 2016 Form 5498-SA minus any amount in box 3 of your 2015 Form 5498-SA. These forms would have been mailed to you (assuming that some amounts were deposited in or for 2015 and 2016).
Forms 5498-SA are available in your Wage & Income transcript from the IRS. Your 2016 Wage & Income transcript should still be be available for online download, but I think you would have to obtain your 2015 Wage & Income transcript by mail (although processing of mailed transcript requests is temporarily suspended):
https://www.irs.gov/individuals/get-transcript
It seems that your HSA administrator and HSA trustee are two different entities, with the HSA administrator providing the statements but the HSA trustee providing the Forms 5498-SA. What matters is what the HSA trustee reports and apparently your HSA statements were incorrect.
