There is one Mary Aletta Markoe born probably early 1840s to Hartman Markoe and Elizabeth Cooper Kelly Markoe but my (unsubstatiated) records show she died in infancy.
Hartman Markoe married 2nd and had another child named Mary (middle initial "P." born probably late 1850s). The mother was Penett or Punett.
My information on this line of Markoes is scant but I would say that if your Mary was, indeed, Mary Aletta then there is a good chance she fits in this line somewhere. Mary Aletta was a favorite Heyliger honorific. It was also the name of Hartman Markoe´s mother, Mary Aletta Heyliger.
It was also a Markoe tradition to name a surviving child after one who had died.
As your Mary was in Lousiana in the early 1860s and then (I think you said in another post) lived in Arkansas it´s possible she was somehow connected to the Francis Markoe IV-Maria Thomas Markoe line. Francis IV was an officer for the CSA - the only Markoe line I´ve found that allied with the South. Francis IV was Hartman´s first cousin.
If your Mary Aletta Markoe was from one of these lines then there are probably family traditions regarding their history. Do you know of any? Also, names of children could be a key - Markoes tended to pass the same given names for several generations. As your Mary Aletta died 1923 there should be an official death record that might show her parents.