It is not a 'real' deduction. It is just a way to report your proper income and avoid an IRS notice.
For example, let's say the 1099 says $100,000, but you only received $90,000. For your tax return to be correct, you need to report $90,000 of income because that is what you actually received.
However, the IRS sees $100,000 on the 1099. So to prevent the IRS notice, you could report $100,000, then enter the $10,000 as a deduction to give you the proper reporting of $90,000 of income.
You just need to keep in mind that your tax return needs to report what you actually received, regardless of whatever a 1099 may say. As was pointed out, next year the 1099 won't show that extra amount, so you will need to manually enter that on next year's return because you didn't receive it until 2018.
On the other hand, I don't understand how they already sent a 1099 with the full amount and you received that before January 1st, but you did not receive the check yet. That seems weird.
