I'm assuming you're referring to the Confluence Source Editor.
I don't think there is a supported way to modify the source code, so the answer would probably be "through the normal Confluence editor." Although the marketplace says "Unsupported," the plugin is certainly supported as far as updates (I can imagine Atlassian would be mobbed with outcry if they didn't), but I think what they mean is "if you type something in the source editor and mess up your page, we can't help you."
The only other way I can think of to modify the source is to use the REST API. You could make a GET call to get the page source and then PUT the updated source to update the page content.
Thanks for your clarification, Stephen. That is helpful to know as the concerns my Confluence admin has expressed about the source editor are: 1) It's unsupported; 2) Could lead to corrupted pages; 3) Could cause issues with future upgrades. It looks like I can at least strike the first item from the list.
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