  Consider the Boltzmann equation in the perturbation regime. Since the
macroscopic quantities in the background global Maxwellian are obtained through
measurements, there are typically some errors involved. This paper investigates
the effect of background variations on the solution for a given initial
perturbation. Our findings demonstrate that the solution changes continuously
with variations in the background and provide a sharp time decay estimate of
the associated errors. The proof relies on refined estimates for the linearized
solution operator and a proper decomposition of the nonlinear solution.
