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tokens: of the model with the expected scaling relations described in Section 3.1 using km s −1 from Bernardi et al. ( 2003 ). The expected value is , which is in agreement with the model values in Table B4 , mostly the one of the most complete cluster model. The two other results are closer to the upper limit value because those models do not take in account the impact of the cluster convergence boosting the lensing power of the galaxy, therefore leading to an overestimation of the velocity dispersion of the lens. However the value of of the complete cluster model is ∼40 per cent higher than the one optimized in the cluster model. This could indicate that the standard galaxy is not constrained well enough, as the cluster model not including the GGL constraints provides different values. We find a similar problem in the cluster model of RX J2129 where . If the GGL lens follows the scaling relation as we assumed it, the velocity dispersion of the lens would be , which is far too low according to Fig. 12 to produce multiple images as we observe them even for a source with s = 10. Even with the boost of the cluster, a complete model constraining the GGL parameters with a source with s = 10 leads to a σ 0 = 166.8 . There is a ∼30 per cent variation with this value and the one derived from the scaled standard galaxies in the models presented in Table B2 . Either the standard galaxy parameters are not well constrained or our assumption about the GGL lens is wrong. Having a spectroscopic redshift for the GGL source would provide a way to constrain σ 0 independently of the scaling relation and would allow us to test the consistency of the results. Then, assuming that the galaxy follows this relation, we could constrain better the standard galaxy parameters directly using the locations of multiple images in the GGLs. For this reason, a spectroscopic follow-up of the 24 GGLs presented in Fig. A1 and Table A1 would improve greatly the model constraints for all those clusters. 5 SUMMARY AND CONCLUSIONS We visually inspect the full Hubble field of view of the 25 observed clusters from the CLASH survey in order to locate GGL events in the outskirts of those clusters. We find a selection of 24 candidate GGLs (some already known), and study in detail three of them presenting the following characteristics: a single lens, at least four distinct multiple images, and a separation from the BCG larger than 80 arcsec. For each of those GGLs and their associated cluster, we produce four parametric models of the DM distribution to study the influence of the cluster on the GGL modelling and the influence on the GGL on the cluster models. Through those models, we show that the modelling of the GGLs cannot be done properly without taking into account its environment. This can be achieved through a complete model of the neighbour structures or even with a simple parametrization of their effects like an external shear. A photometric redshift is accurate enough to properly