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 I enrolled in an HSA and made a pre-tax contribution of $3,350 through payroll deductions.

This should be included in 12W of your w-2.  salary reduction is proper because that's where you get the tax deduction when you make HSA contributions through an employer plan. 

Additionally, my employer contributed $500 pre-tax to my HSA account.

that should be added to your contributions and $3850 should be in box 12W 

box 9 on the 8889 should reflect 3850

 

 

you need to contact your employer to get a correct the W-2 and since yours is wrong most likely the W-2 for  every other employee that made an HSA contribution through the employer is wrong.

 

from w-2 instructions

W—Employer contributions (including amounts the employee elected to contribute using a section 125 (cafeteria) plan) to your health savings account. Report on Form 8889.

if your employer refuses you'll have to contact the iRS

see this iRS link

https://www.irs.gov/faqs/irs-procedures/w-2-additional-incorrect-lost-non-receipt-omitted 

calling instructions

  1. Call 1-800-829-1040 between the hours of 7:00 AM – 7:00 PM local time.
  2. Press “1” for English or “2” for Spanish.
  3. Press “2” for “answers about your personal income taxes.”
  4. Press “1” for “questions about a form you have already submitted or a payment or to order a tax transcript.”
  5. Press “3” for “all other questions about your tax history or payment.”
  6. Press “2” for “all other questions about your tax history or payment.”
  7. Do not input your Social Security Number when the recording tells you to.
  8. Press “2” for “personal- or individual-tax related question.”
  9. Press “3” for “all other inquiries.”
  10. Wait to be connected to someone at the IRS.