Nimbostratus
NimbostratusI believe the UI and tmsh have a way to determine if a value was explicitly (or customized) set by referencing the bigip.conf which I'm sure they keep in a parsed object in memory. I don't think the rest API has any way to do this, as it's going to return all available settings so you can see their value (sorta like "all-properties" in tmsh). In order to do what you seem to want, you'd likely need to pull down the bigip.conf itself (and potentially other config files) and parse it locally to make those kind of determinations.
You could also run tmsh scripts via the rest API, I think, which would be a way to see what values are explicitly set for any given object.