I decided to do some further research on my daughter's paternal grandmother. I found the following at The National Archives and thought it quite interesting:

The Dawes Commission rejected nearly two-thirds of the applications for enrollment. Those who were rejected also have census cards and application jackets available for research. NARA's Fort Worth facility has indexes available on microfilm for those rejected as Cherokee or Choctaw. Fort Worth also has the applications of those who applied to the Dawes Commission in 1896, all of which were declared invalid.