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We investigate the influence of attenuation on the speed of erasure of photorefractive gratings by solving the coupled-wave equations in the undepleted pump approximation and by taking into account the attenuation and Gaussian intensity profile of all the beams. The extrinsic grating decay rate is significantly lower than the intrinsic photorefractive decay rate in samples with overall attenuation as low as 10%. The Gaussian beam profiles of the readout and the erasing beams result in a further reduction of the extrinsic decay rate. The results of these calculations are used to determine the spectrum of intrinsic decay rates in a photorefractive polymer.