We combine the recent estimate of the contribution of galaxies to the 3.6 micron intensity of the extragalactic background light (EBL) with optical and near-infrared (IR) galaxy counts to set new limits on intrinsic spectra of some of the most distant TeV blazars 1ES 0229+200, 1ES 1218+30.4, and 1ES 1101-232, located at redshifts 0.1396, 0.182, and 0.186, respectively. The new lower limit on the 3.6 micron EBL intensity is significantly higher than the previous one set by the cumulative emission from resolved Spitzer galaxies. Correcting for attenuation by the revised EBL, we show that the differential spectral index of the intrinsic spectrum of the three blazars is 1.28 +- 0.20 or harder. These results present blazar emission models with the challenge of producing extremely hard intrinsic spectra in the sub-TeV to multi-TeV regime. These results also question the reliability of recently derived upper limits on the near-IR EBL intensity that are solely based on the assumption that intrinsic blazar spectra should not be harder than 1.5.
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