No, you do not need to provide supporting documentation from the charity unless the IRS subsequently asks for it. Your explanation should be sufficient.
If the Form 1099-R shows tax withholding in box 4 and you did not previously report the distribution shown in the Form 1099-R, include copy B of the Form 1099-R with Form 1040X.
(A QCD is an exclusion from income, not a deduction.)
