The measurement of ongoing ice-mass loss and associated melt water contribution to sea-level change from regions such as West Antarctica is dependent on a combination of remote sensing methods. A key method, the measurement of changes in Earth's gravity via the GRACE satellite mission, requires a potentially large correction to account for the isostatic response of the solid Earth to ice-load changes since the Last Glacial Maximum. In this study, we combine glacial isostatic adjustment modelling with a new GPS dataset of solid Earth deformation for the southern Antarctic Peninsula to test the current understanding of ice history in this region. A sufficiently complete history of past ice-load change is required for glacial isostatic adjustment models to accurately predict the spatial variation of ongoing solid Earth deformation, once the independently-constrained effects of present-day ice mass loss have been accounted for. Comparisons between the GPS data and glacial isostatic adjustment model predictions reveal a substantial misfit. The misfit is localized on the southwestern Weddell Sea, where current ice models under-predict uplift rates by approximately 2 mm yr^-1. This under-prediction suggests that either the retreat of the ice sheet grounding line in this region occurred significantly later in the Holocene than currently assumed, or that the region previously hosted more ice than currently assumed. This finding demonstrates the need for further fieldwork to obtain direct constraints on the timing of Holocene grounding line retreat in the southwestern Weddell Sea and that GRACE estimates of ice sheet mass balance will be unreliable in this region until this is resolved.