Remote-sensing products are widely used after disasters as indicators of incurred damage, yet it remains uncertain which mapped surface-disturbance remote-sensing signals are most informative about residential damages. This study examines the damage from the 2023 Cyclone Gabrielle in New Zealand by linking four publicly available remote-sensing layers—SAR-detected standing water, post-event wetness, soil- or silt-related disturbance, and inferred slope-related disturbance—to residential insurance claims from the public insurer at a fine spatial scale. We construct claim-rate and insurance payout outcomes and estimate cross-sectional models, investigating their association with the data from remote-sensing products. The two insurance outcomes capture recorded claim intensity relative to local building stock and the monetary intensity of insured loss. Slope-related disturbance is most strongly associated with claim occurrence and loss variation in hazard-positive rural areas. Wetness-related disturbance becomes the strongest predictor of loss severity once claims are observed. Standing-water and soil-related indicators provide smaller but more stable signals, and their composite index is positively associated with both claim rates and payouts. Urban areas show higher baseline loss levels, whereas rural areas show stronger marginal responses to additional physical disturbance. Our findings show that remote-sensing indicators are not interchangeable hazard proxies. Their value as proxies for disaster damage depends on the physical signal captured, the damage outcome measured, and the settlement context in which damage occurs.