Your bank is right that it may not affect your refund, but since the bank sent a copy of the 1099-SA in 2016 with the code of "2" to the IRS,
go ahead and add the 1099-SA to the 2016 tax return (if it's the second 1099-SA for 2016, then click on "Add Another 1099-SA").
The distribution with a code of "2" will generally not increase your taxable income. If there is an entry in box 2 ("Earnings in excess contributions"), then this amount will be added to your taxable income, but this is usually very little if anything.
