Redrawing those graphs in a vector graphics application - for example Inkscape - should not be that hard and will get you very nice results, especially if you need different sizes where you'd like to do simplifications for them.
This is also most likely how this image was created in the first place, so if you could get the original, you might be a lot better off. Otherwise, I'd take this as a training exercise to learn a vector graphics application.
If you want to stick to GIMP, you could do the following:
Then you can zoom into a border area and use Clear from the Edit menu - a very convenient way to do this is to use its default keyboard shortcut, the Delete key on your keyboard, repeatedly.
This will delete everything that's selected, but due to the soft nature of the feathered selection outline, will only do so gradually along those borders. They will become transparent, the white will go away and they should be a much better fit over different backgrounds.