I work for a non-profit in Thailand and our registration status changed, so this year my employer, a US non-profit, had to pay $56,000 to the Thai Government on my behalf. However, in my W-2 there is no mention of foreign taxes paid. Rather, my employer just grossed up my "wages" and there's no mention of foreign taxes paid. Did my employer make a mistake? If so, how should my employer report foreign taxes paid on my behalf on my W-2?
Your employer reported your W-2 wages correctly. Anything your employer paid to you or on your behalf is compensation to you and is included in your wages. If your employer grossed up the foreign tax component of your compensation, then the employer is paying the taxes on this part of your income.
You can take a foreign tax credit claiming the foreign tax paid by your employer on your behalf on your tax return. You can also choose to take the foreign earned income exclusion to exclude up to $103,900 (for 2018) of your income from US tax if you meet the requirements.
Please see the below IRS Publication for more information regarding the credit and exclusion.