In this paper we study inverse problems about the reconstruction of the space-dependent lumped water-to-air mass transfer coefficient in a model of pollution in porous media. The model is considered as a system of a parabolic PDE coupled with an ODE, and, equivalently, as an advection-diffusion integro-differential equation. We investigate two inverse problems to find the overall mass transfer coefficient, given that information about the contaminant concentration in the gaseous phase is known as a measurement at the final time, or as a time-averaged measurement. They are reformulated as least-squares minimization problems and the Fréchet gradients of the corresponding functionals are derived using the adjoint equation method.