I am not related and my instinct and experience tells me that Maggie May Mitchell Burrow did not really know who Ena's parents were. Maggie was the informant on death certificate.
Birth record found on familysearch.org shows a female Parnell was born in Falls county Texas 25 July 1906 to T E (Theodore/Theo) and N L (Nora)Parnell. Another daughter was born 07 Aug 1905.
T E Parnell married Nora Cline in Falls county 23 Oct 1904 and then they are found in Bosque county 1910 and 1920 census. In 1910 census 2nd daughter's name was spelled "Enard". The 1920 census shows "Aenird" as her name.
Other Parnell children were:
Opal abt 1909
Charles Henry 1913
William Otis 1918
twins Mildred L and Melvin Ernest born 13 Oct 1919.
T E Parnell was born TX abt 1881 and Nora Cline was born abt 1884. On the 10th of Oct 1925 in Bosque county Mrs Nora Parnell married William S Land troop and they are found in 1930 census in Bosque county with Charles, William, Mildred and Melvin.
1940 census finds Nora living with daughter Mildred Harper, wife of Jim Harper, and their daughter Shirley Lorene born 1936.
According to 1930 census in Cooke county Texas, William Mitchell and Ena married abt 1927 and had 2 daughters "Eoner"Pearl in 1928 and Maggie May in 1930.
William was born in Cooke county abt 1874 to James Mitchell and Martha Tinney.
On Maggie's birth certificate it says she was Ena's 3 child. On Ena Pearl's it shows she was first child born .
I also found that there was a child born to an Enna Parnell in Denton county 26 July 1925. Was she the same person? There was a home for unwed mothers there.
No records found for T E Parnell and Nora Cline before their marriage and no death records found by me.
At this point you need a copy of Ena's applicatin for social security number (SS5) to find out who she said her parents were.