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The observed crustal uplift rates in Greenland are caused by the combined response of the solid Earth to both ongoing and past surface mass changes. Existing elastic Earth models and Maxwell linear viscoelastic GIA (glacial isostatic adjustment) models together underpredict the observed uplift rates. These models do not capture the ongoing mantle deformation induced by significant ice melting since the Little Ice Age. Using a simple Earth model within a Bayesian framework, we show that this recent mass loss can explain the data‐model misfits but only when a reduced mantle strength is considered. The inferred viscosity for sub‐centennial timescale mantle deformation is roughly one order of magnitude smaller than the upper mantle viscosity inferred from GIA analysis of geological data. Reconciliation of geological sea‐level and modern crustal motion data may require that the model effective viscosity be treated with greater sophistication than in the simple Maxwell rheological paradigm. Plain Language Summary: There are 57 permanent Global Navigation Satellite System (GNSS) stations on bedrock in Greenland. These stations provide point‐measurements of three‐dimensional crustal motion. We can model a large portion of the observed crustal uplift rates as elastic Earth response to ongoing rates of ice‐mass loss. We model the remaining part of the uplift rates as the ongoing viscous response of the solid Earth to past ice‐ocean mass exchange—a process termed glacial isostatic adjustment (GIA). Earth structure and deglaciation history in GIA models are usually constrained by geological data that record paleo sea level and past ice margins. To fully explain the GNSS‐measured uplift rates, we propose that these geologically constrained GIA models should additionally resolve: (a) ice‐mass changes during and after the Little Ice Age; and (b) broadband mantle relaxation processes. While such features are challenging to implement, they offer a more granular model paradigm appropriate to the improved temporal sampling that the collective geological and geodetic data sets now provide. Key Points: GIA models constrained by geological data underpredict the modern crustal uplift rates corrected for the elastic loading effectsMass loss since the Little Ice Age explains the residual uplift rates provided a reduced mantle viscosity on sub‐centennial timescalesReconciling geological and modern geodetic data requires a more sophisticated mantle rheology model than generally used in loading studies [ABSTRACT FROM AUTHOR]