Does Gimp have sliders? Sliders are often simpler to use than tone curves.
In LR5, there are 2 sliders that have the most direct control over brigtness of highlights - named Highlights and Whites. Highlights reduces the exposure (darkens) the brightest part of the image (shifts the righthand edge of the histogram towards the left (a simplification)), and the Whites adjusts the overall white point (sounds a bit similar result to what sidknee is describing). Playing with those 2 sliders goes a long way towards correcting blown out whites.
In some images (not yours), where the whites are blown in the raw file, you won't be able to bring any detail back from the blown highlights. As you are bringin you highlights up from the original capture, you should be able to get some nice detail in those white feathers.