  We determine the concentration-mass relation of 19 X-ray selected galaxy
clusters from the CLASH survey in theories of gravity that directly modify the
lensing potential. We model the clusters as NFW haloes and fit their lensing
signal, in the Cubic Galileon and Nonlocal gravity models, to the lensing
convergence profiles of the clusters. We discuss a number of important issues
that need to be taken into account, associated with the use of nonparametric
and parametric lensing methods, as well as assumptions about the background
cosmology. Our results show that the concentration and mass estimates in the
modified gravity models are, within the errorbars, the same as in $\Lambda$CDM.
This result demonstrates that, for the Nonlocal model, the modifications to
gravity are too weak at the cluster redshifts, and for the Galileon model, the
screening mechanism is very efficient inside the cluster radius. However, at
distances $\sim \left[2-20\right] {\rm Mpc}/h$ from the cluster center, we find
that the surrounding force profiles are enhanced by $\sim20-40\%$ in the Cubic
Galileon model. This has an impact on dynamical mass estimates, which means
that tests of gravity based on comparisons between lensing and dynamical masses
can also be applied to the Cubic Galileon model.
