Sadly, we often see this problem when it is beyond the cleaning stage and the oils have penetrated deep into the leather, spreading far beyond what can be detected on the surface. Untreated, this can cause the leather to break down and rot, causing irreversible damage.
This was the case with the headrest on a cream leather recliner armchair we treated recently. While on the surface the damage looked minimal, it was necessary to remove the contaminated leather to reveal just how far the oil had spread. The solution? In a small number of cases we can extract the oil and refinish the existing leather, but often we recommend replacing the affected panels, as we did in this instance. Our client was very pleased with the finished result, which can be seen in the photos below.