Chemotactic cells of eukaryotic organisms are able to accurately sense shallow chemical concentration gradients using cell-surface receptors. This sensing ability is remarkable as cells must be able to spatially resolve small fractional differences in the numbers of particles randomly arriving at cell-surface receptors by diffusion. An additional challenge and source of uncertainty is that particles, once bound and released, may rebind the same or a different receptor, which adds to noise without providing any new information about the environment. We recently derived the fundamental physical limits of gradient sensing using a simple spherical-cell model, but not including explicit particle-receptor kinetics. Here, we use a method based on the fluctuation-dissipation theorem (FDT) to calculate the accuracy of gradient sensing by realistic receptors. We derive analytical results for two receptors, as well as two coaxial rings of receptors, e.g. one at each cell pole. For realistic receptors, we find that particle rebinding lowers the accuracy of gradient sensing, in line with our previous results.