Both of my parents wend to colleges that didn't have GLOs. My sister was very anti-Greek when she was at my university, so my parents only saw the bad side. When I decided to go through recruitment, my mom and sister thought I was nuts. After meeting all of my sisters and seeing how great they are, though, my parents and sister realize that it is important to me and has done me a lot of good. My mom even wrote a letter to the View when Alexandra Robbins was on, telling the ladies how my sorority has benefited me and how I was luckier than Barbara, Meredith, and Elisabeth to have experienced Greek Life.
I know a lot of school's Greek Life websites give the statistics about GPAs and involvement. Show her some of those. I am pretty sure the Clemson AXO site has good statistics on it. You can tell your parents that it's not like Animal House, too. Sororities do philanthropy work, encourage academic growth, etc. I hope your parents will support your decision