This paper proposes to exploit gravitational lensing effects to improve the sensitivity of neutrino telescopes to the intrinsic neutrino emission of distant blazar populations. This strategy is illustrated with a search for cosmic neutrinos in the direction of four distant and gravitationally lensed Flat-Spectrum Radio Quasars. The magnification factor is estimated for each system assuming a singular isothermal profile for the lens. Based on data collected from 2007 to 2012 by the ANTARES neutrino telescope, the strongest constraint is obtained from the lensed quasar B0218+357, providing a limit on the total neutrino luminosity of this source of $1.08times 10^{46},mathrm{erg},mathrm{s}^{-1}$. This limit is about one order of magnitude lower than those previously obtained in the ANTARES standard point source searches with non-lensed Flat-Spectrum Radio Quasars.
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