Since the tax reform act of 2017, relocation assistance must be treated as part of your gross income, and is subject to federal and state income tax withholding as well as social security and Medicare tax withholding. The company can't reimburse you tax-free, and if they pay the movers directly, that also has to be included in your gross wages subject to tax.
Without seeing the actual numbers it's hard to know what they did.
Regardless, box 2, 4, 6, and 17 should show the actual tax withheld and credited to your account, regardless of how is was calculated. If you owe tax because less was withheld, then you owe tax. If the withheld taxes don't match your actual paychecks, then the company either needs to refund you the difference (if they took money from your check and did not credit it to your account at the IRS) or the company needs to issue a corrected W-2.
