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Unmanned aerial vehicle-assisted disaster recovery missions have been promoted recently due to their reliability and flexibility. Machine learning algorithms running onboard significantly enhance the utility of UAVs by enabling real-time data processing and efficient decision-making, despite being in a resource-constrained environment. However, the limited bandwidth and intermittent connectivity make transmitting the outputs to ground stations challenging. This paper proposes a novel semantic extractor that can be adopted into any machine learning downstream task for identifying the critical data required for decision-making. The semantic extractor can be executed onboard which results in a reduction of data that needs to be transmitted to ground stations. We test the proposed architecture together with the semantic extractor on two publicly available datasets, FloodNet and RescueNet, for two downstream tasks: visual question answering and disaster damage level classification. Our experimental results demonstrate the proposed method maintains high accuracy across different downstream tasks while significantly reducing the volume of transmitted data, highlighting the effectiveness of our semantic extractor in capturing task-specific salient information.