Looking for Great Grandma

My great grandmother was named Ora D Greer b.1915 Oklahoma and listed as black in census. Her son, my grandfather, Kenneth L Barr b.1955 (who was adopted/born in Texas by Ora’s husband, Earl Barr) did not know his father and reported that ‘the Native American side of the family’ had little contact with him and his mother. He told us we were Cherokee. I am trying to figure out if there is any credence to this, but my mother and Aunt believe this to be very true based off of the stories he shared with them. I know Ora’s Parents last names were Toles (Father/listed as born in Oklahoma) and Greer (listed as born in Texas) and I have no first names. I know he had a cousin named ‘Lola’ in Oklahoma.