This problem seems to have been asked before without a satisfactory solution. There is no way of building for windows and mingw currently distributed with TBB.
I've tried to make my own inc files to get it working but I am, how you say, bad at it.
I have an angle on how it could be done, but I'd appreciate it if a more skilled person either helped or did it himself. If I knew what TBB required of the compiler and how to satisfy those needs via GCC, this would be trvial. Alas, the inc files are a little opaque to my amateur eyes.
I know of one issue, that is that the windows inc file called detect.js. The thing is, this script gets information like the runtime version by calling the VC++ compiler. Not good. I'm not sure how to get such info for MinGW and the linux gcc inc isn't very helpful.
Basically the inc files have to be spliced together; part linux gcc, part windows cl. I don't know how to do it.
I do know that mingw uses the same runtime as VC++, so it should be possible with a little work.