We investigate the effect of Coulomb scattering from trapped charges on the mobility in the two-dimensional channel of an organic field-effect transistor. The number of trapped charges can be tuned by applying a prolonged gate bias. Surprisingly, after increasing the number of trapped charges to a level where strong Coulomb scattering is expected, the mobility has decreased only slightly. Simulations show that this can be explained by assuming that the trapped charges are located in the gate dielectric at a significant distance from the channel instead of in or very close to the channel. The effect of Coulomb scattering is then strongly reduced.