Compensating for group velocity dispersion is an important challenge to achieve stable midinfrared quantum cascade laser (QCL) frequency combs with large spectral coverage. We present a tunable dispersion compensation scheme consisting of a planar mirror placed behind the back facet of the QCL. Dispersion can be either enhanced or decreased depending on the position of the mirror. We demonstrate that the fraction of the comb regime in the dynamic range of the laser increases considerably when the dispersion induced by the Gires-Tournois interferometer compensates the intrinsic dispersion of the laser. Furthermore, it is possible to tune to the offset frequency of the comb with the Gires-Tournois interferometer while the repetition frequency is almost unaffected.