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We study the scattering of solitons from an impurity in the framework of the discrete nonlinear Schrödinger equation with a saturable nonlinearity. We show that this model displays a complex scenario compared to the same equation with cubic nonlinearity. For instance, even considering a single value of the soliton speed and frequency, one can generally observe the existence of a reflected and a transmitted soliton after the interaction between the incoming soliton and the impurity, and that in the case of an attractive impurity, a trapped soliton can coexist with the reflected and transmitted ones. [ABSTRACT FROM AUTHOR]