The months of 'Id are not incomplete. And in the hadith narrated by Khalid (the words are):" The months, of 'Id are Ramadan and Dhu'l-Hijja."
أَنَّ نَبِيَّ اللَّهِ ﷺ قَالَ شَهْرَا عِيدٍ لاَ يَنْقُصَانِ فِي حَدِيثِ خَالِدٍ شَهْرَا عِيدٍ رَمَضَانُ وَذُو الْحِجَّةِ