^^^ What she said.
I wouldn't worry too much about the app. Most Big XII schools have decently strong Greek systems where my reasoning for liking Greek family members wouldn't apply. The applications can be customized for each campus, so apparently this campus chose to ask about sister, mother, grandmother only. No biggie!
And it probably wouldn't hurt to go ahead and ask about connections at this time. I wouldn't ask for recs yet - but if you find out through casual conversation that a teacher, mentor, friend of family is a member of a sorority, go ahead and say that you've been considering recruitment and would love to hear about their experience. Then when the time comes, they may offer to write one for you, and you don't even have to ask. Plus they'll know more about you and can write a better letter....