We consider the inverse acoustic time domain scattering problem for absorbing scatterers modeled by impedance boundary conditions. We present and analyze a factorization method for reconstructing the obstacle boundary from far field measurements. The analysis is based on using the Laplace transform and proving the coercivity of the solution operator in suitable weighted spaces in time. This leads us to consider a modified far field operator parameterized by the imaginary part of Laplace variable which is different but can be arbitrarily close to the original far field operator. As a proof of concept we also provide some preliminary numerical examples to test and discuss the effectiveness of the resulting inversion method when applied to the original far field operator.