Viscoelastic rebound of the solid Earth due to the removal of ice loads has the potential to delay marine ice sheet retreat through a reduction in local sea level. Thwaites Glacier, Antarctica, has the potential for rapid retreat because it lies in a large overdeepened marine basin. However, this region of West Antarctica has a particularly low mantle viscosity and thin lithosphere, potentially leading to a significant negative feedback between ice loss and bedrock uplift. In this study, we assess the impact of solid-earth rheological structure on model projections of the retreat of Thwaites Glacier, West Antarctica, and the associated sea-level rise contribution by coupling the dynamic ice sheet model MALI to a regional glacial isostatic adjustment (GIA) model. We test the sensitivity of 500-year model projections of ice-sheet retreat to four solid-earth rheologies, forced by standard ISMIP6 ocean and atmospheric datasets for the RCP8.5 climate scenario. For the mantle viscosity best supported by observations, the negative GIA feedback slows grounding line retreat after 500 years by 137 years and reduces mass loss by 19% relative to control simulations without GIA. For the weakest solid-earth rheology consistent with observations, the delay in glacier retreat after 500 years is 263 years and mass loss reduction reaches 72%. At the same time, we estimate that water expulsion from the rebounding solid Earth beneath the ocean near Thwaites Glacier may increase the sea-level rise contribution of Thwaites Glacier by up to 20% after 500 years, partially counteracting the negative GIA feedback to glacier evolution. We hypothesize that the strength of the feedback between the solid Earth and ice sheet is determined by a competition between the spatial extent and timescale of bedrock uplift relative to the rate retreat of grounded ice away from the region of most rapid uplift. Although limited constraints on solid-earth rheology leads to large uncertainty in future sea-level rise contribution from Thwaites Glacier, under all plausible parameters for this region the GIA effects are large enough to be important to include for future projections of Thwaites Glacier of more than a century.