  Observations of very-high-energy (VHE, E > 250 GeV) gamma-ray emission from
several blazars at z > 0.1 have placed stringent constraints on the elusive
spectrum and intensity of the intergalactic infrared background radiation
(IIBR). Correcting their observed VHE spectrum for gamma-gamma absorption even
by the lowest plausible level of the IIBR provided evidence for a very hard
(photon spectral index Gamma_{ph} < 2) intrinsic source spectrum out to TeV
energies. Such a hard VHE gamma-ray spectrum poses a serious challenge to the
conventional synchrotron-self-Compton interpretation of the VHE emission of TeV
blazars and suggests the emergence of a separate emission component beyond a
few hundred GeV. Here we propose that such a very hard, slowly variable VHE
emission component in TeV blazars may be produced via Compton upscattering of
Cosmic Microwave Background (CMB) photons by shock-accelerated electrons in an
extended jet. For the case of 1ES 1101-232, this component could dominate the
bolometric luminosity of the extended jet if the magnetic fields are of the
order of typical intergalactic magnetic fields B ~ 10 micro-Gauss and electrons
are still being accelerated out to TeV energies gamma > 4 X 10^6) on kiloparsec
scales along the jet.
