Haha it's all comming together now - if you're saying that the stain comes back after H2O2 (Hydrogen-Peroxid) and the literature is correcting in saying that the thyroid utilizes hydrogen peroxide to convert Iodine forms, that it seems that the H2O2 (Hydrogen-Peroxid) oxidizes the halogenated fatty acids and liberates the Iodine from the fatty acid layer.
So it is possible that staining the skin may only trap the Iodine the layer and only slowly absorbed/if any absorption at all; interesting