Geophysical turbulence is strongly influenced by the variation of the Coriolis force with latitude (β-effect): when this effect is significant an anisotropic inverse cascade is developed since energy is preferentially transferred towards zonal modes. The consequent emergence of flow structures along the zonal direction can strongly impact turbulent transport and modify meridional scalar diffusion. In this letter we investigate zonal and meridional diffusion in laboratory experiments of turbulence affected by aβ-effect. The degree of anisotropy and the flow characteristic scales have been quantified according to a Lagrangian approach based on the reconstruction of tracer trajectories, i.e., in analogy with oceanic drifters data, and on the Finite-Scale Lyapunov Exponent (FSLE) analysis. An experimental confirmation of a recently introduced scaling law for the meridional diffusion in the marginally zonostrophic regime is also presented.