Grease, as used for lubrication of rolling bearings, is a two-phase organogel that slowly releases oil from its gelator matrix. Because the rate of release determines the operation time of the bearing, we study this release process by measuring the amount of extracted oil as a function of time, while we use absorbing paper to speed up the process. The oil concentration in the resulting stain is determined by measuring the attenuation of light transmitted through the paper, using a modified Lambert-Beer law. For grease, the timescale for paper imbibition is typically 2 orders of magnitude larger than for a bare drop of the same base oil. This difference results from the high affinity, i.e. wetting energy per unit volume, of the oil for the grease matrix. To quantify this affinity, we developed a Washburn-like model describing the oil flow from the porous grease into the paper pores. The stain radius versus time curves for greases at various levels of oil content collapse onto a single master curve, which allows us to extract a characteristic spreading time and the corresponding oil-matrix affinity. Lowering the oil content results in a small increase of the oil-matrix affinity yet also in a significant change in the spreading timescale. Even an affinity increase of a few per mill doubles the timescale.