The spectral energy distributions (SEDs) of some T Tauri stars display a deficit of near-infrared flux that could be a consequence of an embedded Jupiter-mass planet partially clearing an inner hole in the circumstellar disc. Here, we use two-dimensional numerical simulations of the planet-disc interaction, in concert with simple models for the dust dynamics, to quantify how a planet influences the dust at different radii within the disc. We show that pressure gradients at the outer edge of the gap cleared by the planet act as a filter - letting particles smaller than a critical size through to the inner disc while holding back larger particles in the outer disc. The critical particle size depends on the disc properties, but is typically of the order of10μm. This filtration process will lead to discontinuous grain populations across the planet's orbital radius, with small grains in the inner disc and an outer population of larger grains. We show that this type of dust population is qualitatively consistent with SED modelling of systems that have optically thin inner holes in their circumstellar discs. This process can also produce a very large gas-to-dust ratio in the inner disc, potentially explaining those systems with optically thin inner cavities that still have relatively high accretion rates.