  Extended theories of gravity have been extensively investigated during the
last thirty years, aiming at fixing infrared and ultraviolet shortcomings of
General Relativity and of the associated $\Lambda$CDM cosmological model.
Recently, non-local theories of gravity have drawn increasing attention due to
their potential to ameliorate both the ultraviolet and infrared behavior of
gravitational interaction. In particular, Integral Kernel theories of Gravity
provide a viable mechanism to explain the late time cosmic acceleration so as
to avoid the introduction of any form of unknown dark energy. On the other
hand, these models represent a natural link towards quantum gravity. Here, we
study a scalar-tensor equivalent model of General Relativity corrected with
non-local terms, where corrections are selected by the existence of Noether
symmetries. After performing the weak field limit and generalizing the results
to extended mass distributions, we analyse the non-local model at galaxy
cluster scales, by comparing the theoretical predictions with gravitational
lensing observations from the CLASH program. We obtain agreement with data at
the same level of statistical significance as General Relativity. We also
provide constraints for the Navarro--Frenk--White parameters and lower bounds
for the non-local length scales. The results are finally compared with those
from the literature.
