I've done graduate admissions for a while at a... well, suffice it to say, "higher ranked" (whatever that means) school than UGA. No, I don't care if your grades in "Poetry for Perfectoids" suck, or "Machiavelli for Morons". Just please don't have your grades in statistics (i.e. graduate level probability, etc.) classes that suck if you say you're interested in working in probability in your statement, etc. By and large people in my department on graduate admissions share my philosophy, and many of my coauthors at similarly ranked schools feel the same way, although your mileage may vary depending on who specifically reads your application.

EDIT: My goal in posting  on this site is to communicate helpful answers without having to deal with couching in my answers in politically correct nonsense. The last time I had my name attached to one of my answers on a certain practice in the profession (not on this site, but elsewhere on the internet), I got tons of nonsense I did not want to deal with for not couching my answer in a more politically correct fashion. How many times must one qualify their answers so that their younger and supposedly more empathetic towards those junior to themselves colleagues find it acceptable? So that is why I am anonymous on this site.

When I mean "I don't care" here, it means that it does not affect an applicant adversely, for the purposes of admissions or likelihood of receiving the more selective extra money you alluded to if their non-math GPA is lower (bar the exceptional cases I mentioned above). Conversely, if you have a perfect non-math GPA, great, more power to you, but it won't really affect my decision to admit/reject, give you the extra money, etc. And yes, while most people we admit have great track records all across the board, we do quite frequently admit those with crappy grades in non-math courses.