Thankfully, this is not an issue on my land, however I was curious whether there were specific raptors which might target these or similar critters and I found this:
Ground squirrels play an important role in the ecology of Alberta’s wildlife. Ground squirrels are a major source of food for many predatory birds, mammals and reptiles.
One species of raptor, the ferruginous hawk, depends almost entirely on ground squirrels to fledge their chicks.
Similarly, many other species rely on ground squirrels as a major food source
This was from:
https://www1.agric.gov.ab.ca/$department/deptdocs.nsf/all/agdex3471/$file/684-2.pdf?OpenElement
and clearly the Alberta government agencies aren't on the permaculture page yet, so please ignore any of the inappropriate suggestions!
So that brings us to Ferruginous hawks and a different level of government:
Habitat
Ferruginous Hawk requires open habitat, including grassland, shrub-steppe, or desert, typically nesting on elevated features such as trees or nest platforms. Nesting density and the likelihood of re-using nests between years is higher in landscapes with less than 50% cropland. The availability of preferred nesting and wintering habitat has declined by over 80% historically and continues to decrease.
From:
https://www.canada.ca/en/environment-climate-change/services/species-risk-public-registry/cosewic-assessments-status-reports/ferruginous-hawk-2021.html
So maybe by building some nest platforms, you could help an endangered hawk and limit your ground squirrel problem at the same time? I realize you're in the US, but last I saw, birds didn't pay that much attention to borders, so it's more determining whether or not you're in their range.
Grey squirrels are a non-indigenous species in my area and I have a friend who shoots them and either eats them himself, or feeds them to various neighborhood owls. I'm hoping he'll make me a couple of owl nest boxes, but we'll see.