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We present a map of the total intrinsic reddening across ~34 deg$^{2}$ of the Small Magellanic Cloud (SMC) derived using optical ($ugriz$) and near-infrared (IR; $YJK_{\mathrm{s}}$) spectral energy distributions (SEDs) of background galaxies. The reddening map is created using a subsample of 29,274 galaxies with low levels of intrinsic reddening based on the LePhare $χ^{2}$ minimisation SED-fitting routine. We find statistically significant enhanced levels of reddening associated with the main body of the SMC compared with regions in the outskirts [$ΔE(B-V)\simeq 0.3$ mag]. A comparison with literature reddening maps of the SMC shows that, after correcting for differences in the volume of the SMC sampled, there is good agreement between our results and maps created using young stars. In contrast, we find significant discrepancies between our results and maps created using old stars or based on longer wavelength far-IR dust emission that could stem from biased samples in the former and uncertainties in the far-IR emissivity and the optical properties of the dust grains in the latter. This study represents one of the first large-scale categorisations of extragalactic sources behind the SMC and as such we provide the LePhare outputs for our full sample of ~500,000 sources.