Sorry for the delay as I took a break from family research for two years.My partner, Jimmy, is your cousin.
Your great-grandmother's maiden name was Williams.I'm not sure of the exact spelling of her first name but it's spelled "RTISHA" (yes, all capital letters) in one of Bud's sister's social security application of which I have a copy.It looks like it might have been "R.TISHA" but it's hard to tell.
Your great-grandfather Robert Hugh Reed was born in Feb 1865 in GA, most likely Troup County.Rtisha was born Jan 1872 in TX.
Robert's parents were William R. and Milly L. (maiden name unknown).They were also born in GA before 1845 and died sometime before 1880.In the 1880 census Robert and his sister, Lula, are living with their uncle John B. Reed and his wife Martha Caroline Cleborne.Incidentally, Lula married Rtisha's brother Sam.They are in Hill County, TX by the 1870 census.
Rtisha's parents were William Henry Williams and probably Martha Morris (the mother hasn't been proven yet).William was born 07 Apr 1837 in Neosha, Newton Co., MO and died 03 Mar 1925 in Seymour, Baylor Co, TX.
Please let me know if you want more information.I have a bit more information thanks to one of the Reed cousins.