IMPORTANT CORRECTION
Thinking about this some more, I realize that I got it wrong. The company paid out $10,000, $7035 to you and $2,965 to the government, and they should get their full $10,000 back. If they're only asking you to pay back $7,035, they must be making an adjustment in their payroll tax payments so that they get the $2,965 of withheld tax back from the government. Then it's as if they never paid the $10,000 in the first place. In that case, your W-2 should be the same as if they never paid the $10,000 and they never withheld the $2,965. So the $2,965 is not included in the withholding on your W-2 (since the government doesn't have it), and you don't get credit for it on your tax return. But you and the company both come out even. You don't have any taxable income on your W-2 that you didn't actually receive, and you don't get credit for any tax that was not actually withheld. Your refund will be the same as if you never got the relocation payment. You don't owe any additional tax, and you don't get a larger refund.
Also, I've been talking about this as if the entire $2,965 is federal tax. But maybe some of it is state tax. ($2,965 is kind of high for just federal withholding on $10,000.) If so, it doesn't really change anything. The basic idea is the same. It just means that there are two governments involved instead of only one.
Sorry about the confusion. Obviously this is a somewhat complicated situation. You might want to go over it with a local accountant to make sure it's all done right.
You should still discuss it with the payroll department, but what you're looking for is a little different from what I said before. You still want to make sure that the $10,000 gets backed out of your total gross pay for the year. You don't want to have to pay tax on that. But you should also expect that the extra $2,965 gets backed out of your total withholding. The final result is the same as if the company never paid the $10,000.
