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We determine the conditions for which the constraints from lunar laserranging on the time evolution of the local gravitational constant can beextrapolated to impose constraints on the time evolution of the cosmologicalgravitational constant in scalar-tensor theories of modified gravity. We allowfor the possibility that the scalar-tensor theories are non-linear and containa screening mechanism. This results in strong constraints on the running of thecosmological Planck mass described by the Horndeski function$|\alpha_M|\lesssim 0.002$. We find that our assumptions are valid for mostVainshtein and kinetic screening models, where the shift symmetry$\phi\rightarrow\phi + c$ holds, but are violated by some Chameleon andSymmetron screening models, where the macroscopic equivalence principle isbroken.

Constraining the cosmological evolution of scalar-tensor theories with local measurements of the time variation of G