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 sea-level 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.