To gross up means that you were paid more than you actually received so it would cover the taxes. Basically they paid you almost $9k and gave $2,632 to the IRS for you as a withholding like they withhold taxes on your regular wages and gave the other $6,245 to the school for your tuition.
If they wouldn't have "grossed up" your income, then you would have had to pay the taxes on your own on the taxable portion of the tuition assistance.
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