> I'm wondering why you are trying to get that color. 
This is best explained with reference to the attached screen segment. The blue arrow button is a square SVG rendering. The rendering requires that I specify a background color and this needs to be the same as the tab background if it is to look like a triangular button (which is what I want) and not a triangle on a gray square (or some other color). If the background color is determined by a style sheet then it should be possible to query it.

> I think that the best thing to do is to always assume that containers are 
> transparent and whatever background color is visible is just what is underneath
> but it is not the real background color of the container.
My researches have lead me to believe otherwise. The following file (part of the Win7 SDK) is the Aero style sheet.
C:\Program Files\Microsoft SDKs\Windows\v7.1\Include\AeroStyle.xml
If you look in this file you can find a section <class name="TabStyle"> with various sub sections, as for example:
<part name="Body">
    <colorhints>
        <FillColorHint>244 244 244</FillColorHint>
   </colorhints>
</part>
This seems to be the specification for the TabControl colors.
The following article shows how it is possible to query the current theme styles using a .Net API.
http://stackoverflow.com/questions/4198500/in-wpf-how-do-i-get-the-current-themes-button-background
I am thinking it may be possible to access this with a C++/CLI function compiled using the /clr flag. But I am wondering if it will be possible to link with the Eiffel build. Can you offer some advice on this?

As regards GTK themes: I use GNOME themes on Ubuntu and I haven't found any problem with my application. {EV_STOCK_COLORS}.color_dialog returns the correct color and my triangle looks like a triangle.