[AZTheta]

Here's an approach to answering your question that might work: "work backwards" from the information you have. Narrow your field/scope of inquiry. Define the problem and simplify the parameters.

Starting point for me would be to look at published obituaries (often those will contain a reference to greek membership). Then I'd move on to what college(s) grandparents attended, and what years, to find out what sororities/fraternities were active on campus at that time. Check yearbooks online. Check alumnae associations. Contact HQ for various sororities/fraternities active on those campuses with politely worded letters (or emails) explaining your genealogy search and requesting information as to whether any members are in their database that have the same name. And so on.

There's a plethora of information on the internet. You have some time on your hands (don't we all? 2020 just sucks, thanks, Covid-19) and it's an interesting rabbit hole to fall down. There are some members here on GC who are well versed in research and may have other suggestions on what to pursue in your quest for information on your grandparents. Just apply research methodology (assuming you have been taught that in college) and you may find the pot of gold at the end of the rainbow. This isn't the instant answer you seek; IMO it's much more rewarding to actually engage in thinking and problem solving. Aside: did you know that certain areas of the human brain are atrophying due to reliance on technology? Yeah. It's true. You can google it (hahaha I'm so funny).

A final word of advice: be patient, polite, persistent. When you want honey, don't kick the beehive.