The dynamics of the anisotropy of grid-generated decaying turbulence in a rotating frame is experimentally investigated by means of particle image velocimetry on the large-scale 'Coriolis' platform (LEGI, Grenoble). Turbulence is generated by rapidly towing a grid along a channel, providing a nearly homogeneous and isotropic initial state. Various integral scales are computed in order to characterize the growth of the anisotropy during the decay. As expected, the vertical correlation (aligned with the rotation axis) of the horizontal velocity is found to grow more rapidly than the others correlations. More surprisingly, a non trivial hierarchy between the remaining lengthscales is observed, as the consequence of Ekman pumping induced by the vertical confinement.