Your Form 1099-R, which you receive from your IRA custodian, will not reflect anything other than a distribution, so you will need to make the adjustment on your tax return, deducting the amount that was distributed to the charity from the taxable IRA distribution amount (line 15b on your Form 1040).
Frequent reasons the IRS notices are not correct is that the IRA distribution is not taxable because it is an indirect rollover, a recharacterized Roth conversion, a previously taxed excess contribution or deferral, or even a correctly reported Qualified Charitable Distribution or one to a Public Safety Officer.