We incorporate non-Markovian profiles and Linear Response Theory to analyze memory effects in two-band topological quantum systems. Furthermore, we have applied a measure of non-Markovianity in terms of nonlinear optical spectroscopy. On the other hand, we resort to memory kernel, solve the integro-differential equation of the open two-band topological quantum system to describe the degrees of non-Markovianity, calculate response factors based on Linear Response Theory, and analyze non-Markovian dynamics by varying the parameters of the nonlinear spectroscopy environment of the respective open quantum system.