Using a dynamical cluster quantum Monte Carlo approximation, we investigate the
d-wave superconducting transition temperature
Tc in the doped two-dimensional repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings ${t}^{\ensuremath{'}}$ and
t in the form of a checkerboard pattern where
t is the hopping within a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette, and ${t}^{\ensuremath{'}}$ is the hopping between the plaquettes. We find inhomogeneity suppresses
Tc. The characteristic spin excitation energy and the strength of
d-wave pairing interaction decrease with decreasing
Tc, suggesting a strong correlation between these quantities.