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You didn't give any dates, or approximate dates, for those in your query, so I'm not sure if this is a match.Combined info from TX Dth Idx Online and SSDI:
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George Rayburn Moore, b 3 Jul 1912; d 18 Sep 1982 Anderson Co, TX; last residence Palestine, Anderson Co, TX; SS card issued in TX.
Your gr gr grdmthr named Sutton; was Sutton her married name, or her maiden name?Her death record would be under her married name.
Do you know when and where Burt died?You can obtain a copy of his death certificate, which should show the names and birth locations of his parents.
If the above is your Rayburn, then look for his father Burt on the 1920 census when Rayburn would be about 8 years old.