There are two methods, neither one is perfect.
One, just leave it off. The IRS will definitely send a letter saying "you forgot to report some income" and you would answer with a letter explaining that this was a settlement for construction damages, and reduces your basis in the home but is not taxable.
Or two, enter the 1099-MISC (make sure that the money is in box 3, not box 7, and you indicate this is a settlement so you don't get taxed for self-employment as well. then go back into other miscellaneous income an enter an item for "adjustment for non-taxable damage award" of negative or minus $9000. That will offset the income. That should also stop you getting the letter that says "you forgot to report a 1099-MISC form" but it doesn't necessarily mean you won't get a different letter asking you to explain the negative adjustment.