I have taken several classes in several community colleges as an affordable way to complete my gen-ed requirements. I was a naive freshman back then and I thought that since the grades would not transfer to my degree institution but only credits, my grades do not matter much. I ended up doing the bare minimum for the classes and getting a BC for an intro-chem class, and a B for calc 3. These are not reflected on my main transcript, which is right now 3.96 overall.
I am a physics and applied math major in my junior year, and I tend to do satisfactory in my major-related classes (mostly A’s), and I want to apply to grad school after graduation. I recently realized that I need to submit all of my transcripts from every institution I go to, so I am really bothered if my lack-of-focus on these summer courses will do me wrong.
It really depends on the program/school and what the policies are. Every school is different, even for the same degree.
I don’t think that one C will matter much, especially because it is in a gen ed course and your overall gpa is very good. This is just my opinion, as I do not know where or what you are applying to, how competitive the program is etc.
I do think you will be fine, but you can always try and speak to current students and ask.
Also keep in mind that for some degrees, an impressive CV can make up for a less than stellar grade. Also- the longer you are out of school, the less grades matter because they have more to evaluate you on (may not be true all the time).
You will have to supply transcripts from all colleges so the grades will be seen. The impact will depend on the school and the program. However, one C should not be a deal-breaker.