Traditionally, graphical terminal emulators offered 16 (8 and their bright counterparts) colors – in addition to the default foreground and background colors. These are the ones most applications pick from, and the ones whose exact RGB values are configurable in the dialog you show.
Later this was extended to a 256-color palette (the same 16 + 240 new ones (a 6*6*6 color cube and 24 grayscale values)). These are also configurable, but not via the graphical settings of Terminator. You can alter these values using the OSC 4 escape sequence, e.g.
echo -ne '\e]4;16;#123456\e\\' to set palette index 16 to RGB #123456. Verify by
echo -e '\e[38:5:16mtest\e[m' which prints "test" in this color. The index goes from 0 to 15 for the legacy values, and from 16 to 255 for the extended ones. (Also note that OSC 4 takes effect retroactively on text already printed using this color palette index, that is, a newly issued OSC 4 with another RGB value recolors the previously printed "test".)
In practice, however, these new 240 colors aren't typically reconfigured, and have the exact same RGB values across most terminal emulators. Probably redefining them isn't the best approach.
Most likely the syntax highlighting of your editor – or wherever you took that screenshot – uses these extended colors, that's how you get that light green. In addition to reconfiguring the 256-color palette, another approach is to modify the syntax highlighting to use different colors, or to avoid using the extended palette. For the latter, exporting
TERM=xterm instead of
TERM=xterm-256color might be a workaround, as it claims that the terminal only supports 8/16 colors instead of 256, and your editor will probably pick a different color scheme which doesn't use extended colors.
Some terminals, including Terminator also supports direct true colors. If your text editor switches to light green using direct RGB values (without referring to one of the 256 palette colors), there's no other way to change it than change the actual RGB values in the editor's configuration.