You don't get a check, you don't pay New Jersey, there is no exchange of money, and New York does not pay New Jersey. Basically New York gets the tax on the income you earned in New York. On your New Jersey tax return the New York income will be included in your taxable income. But you will get a credit towards your New Jersey tax for part or all of the tax that you paid to New York. The credit is subtracted from your New Jersey tax so you are effectively not paying New Jersey tax on your New York income. The credit is called the Credit For Income Taxes Paid to Other Jurisdictions. It's on line 42 of Form NJ-1040.
