Object retrieval in 3D scenes remains difficult when queries combine hierarchical context, attributes, negation, and chained spatial relations. Existing semantic maps, scene graphs, and agentic memory support open-vocabulary retrieval, but jointly resolving these constraints remains challenging. In this work, we propose INHerit-SG, an incremental hierarchical semantic scene graph with an accompanying retrieval method for complex embodied retrieval. Asynchronous geometric and semantic processing and structural event-driven maintenance organize observations into a hierarchy whose node semantics and spatial relations are recorded as natural language text. The same memory supports direct reading and reasoning by more capable language models or query parsing followed by structured retrieval. Controlled comparisons show that direct reading is more accurate with powerful hosted models, while structured retrieval improves the accuracy of smaller local models and lowers per-query API cost for hosted models. We also construct HM3DSem-SQR, containing 6,084 queries from 36 HM3D-Sem scenes, and evaluate on Main-864, a class-balanced subset spanning all 36 scenes, and in three real-world environments. Experiments show that INHerit-SG outperforms the strongest baselines in both simulator and real-world evaluations. The largest gains come on attribute and compositional queries (7.6 and 6.3 strict Top-1 points on Main-864), with a 9.8-point overall success margin on real robots. Project Page: https://fangyuktung.github.io/INHeritSG.github.io/

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