My wife's Mother died 12/2016 and my wife inherited some CDs. Some of the reported 1099-int interest was paid to her mother. Must she claim this interest?

Yes, any interest o the CDs up to the date of death should have been included on the final decedent's return.  Any income after the date of death should have been sent under a 1099-INT in your wife's name and she would have to include it on her income tax.