Simply buy two small clips that fold over themselves, pin them where you want them and remove one of the metal clip "handles" clips by pinching it.
The shape of the remaining "handle" will hold the palette in place, essentially jamming it against the main stem and one of the wings. The palette and now withstand small gusts of wind, ensuring you wont have to retrieve it from the bushes. Or even worse, from the shirt of a curious onlooker or the face of some kid that is slowly driving you crazy.
No need to fiddle about with the clips either when closing the lid, since they flip over! Just make sure you clean the area from paint.