Solicit a certified SSN from the surviving owner. For 2016, report all of the interest paid prior to the date of death to the decedent and all of the interest paid after the date of death to the survivor. (Required, not a suggestion.) As for the time deposit itself, close it out and reissue it in the name of the survivor for the remaining term or allow him or her to cash it.
If you cannot get a certified SSN from the new owner, then simply remove the incorrect SSN. In the absence of a TIN for information reporting, impose backup withholding. They will come around.