She can appeal to the national office of the sorority. She can sue. Or she can drop the matter recognizing these are close-minded tyrants she really doesn’t want in her life.
Apparently this is a local service sorority so there is no national organization to review an appeal.
Here is a description of the sorority on Cornell’s website:
http://www.cornellcollege.edu/greek-life/fraternities-and-sororities/delphis.shtml
The website of the sorority itself:
http://cornelldeltaphidelta.weebly.com
Why would she want them in her's?