I expand my tutorial to include some additional instructions for people using GIMP, which is available on more platforms than Paint.NET.
@Paul2 Thanks for your suggestion!
Separating the background:
The steps are very similar, so this GIF should be enough:
Creating the grid:
Make sure you create the grid on a distinct layer to be able to modify (resizing, moving etc.) the grid separately.
You can either use the colour picker to determine the grid colour before you open the grid dialogue or you use the colour picker in the dialogue; in that case you will have to change to the layer containing the original diagram.
Separating the forground:
Hide every layer that you do not want to export by pressing the eye symbol.
You have to export as .png to preserve the transparency.
I hope that will help beginners who are not able to use Paint.NET.