A couple of web service calls to the Gainsight API should allow you to do whatever you want.

ahmedA - Thanks for the reply. Is this actually possible? The problem I have is the Gainsight team is a totally different team. I am trying to set up a meeting with them, but it was very unclear in the Gainsight API documentation I read if this is an open API. They also have the SFDC edition and the NXT Gainsight platform, which seem to have different API capabilities. Just curious if this is something that you have had any success with and if so, which 'platform'.
Configure External Action from Gainsight
API Integrations

You'll first need to figure out the data you want to send/pull from Qualtrics, along with the objects you need to update/reference, ONLY then will going through the API docs provide you the appropriate commands. I've seen how Gainsight works with AWS, so working with Qualtrics shouldn't be any different.

Thanks, ahmedA. I think even before that, I need to know if Gainsight is able to send some event to Qualtrics. I'm not looking to pull data out of Qualtrics, but rather send data to Qualtrics.
Perhaps I'm thinking about this wrong though based on your comment. Maybe the way to go would be to send data to Gainsight and have the Qualtrics survey sent from Gainsight.

Oh! In that case you are on the wrong community. It appears you'll need to see what's possible in Gainsight, rather than Qualtrics.

Nah, never the wrong community. I'm on both. I need someone that has worked with both Gainsight and Qualtrics, which is probably not too common, but that's why I'm here. Lots of folks in this community are very creative in solving problems so worth a shot.

@MikeB Did you ever get this solved? I’m looking to do the same.

@etc11b Thanks for resurfacing this thread! I have a contact at Gainsight I can ask -- let me reach out and see if I can find some more intel. Thanks! 

@Michael_Cooksey Awesome! Thank you!

Did anyone ever have any luck digging into Gainsight + Qualtrics API and what it can yield?