Knowledge graphs (KGs) provide structured evidence that can ground large language model (LLM) reasoning for knowledge-intensive question answering. However, many practical KGs are private, and sending retrieved triples or exploration traces to closed-source LLM APIs introduces leakage risk. Existing privacy treatments focus on masking entity names, but they still face four limitations: structural leakage under semantic masking, uncontrollable remote interaction, fragile multi-hop and multi-entity reasoning, and limited experience reuse for stability and efficiency. To address these issues, we propose PrivGemo, a privacy-preserving retrieval-augmented framework for KG-grounded reasoning with memory-guided exposure control. PrivGemo uses a dual-tower design to keep raw KG knowledge local while enabling remote reasoning over an anonymized view that goes beyond name masking to limit both semantic and structural exposure. PrivGemo supports multi-hop, multi-entity reasoning by retrieving anonymized long-hop paths that connect all topic entities, while keeping grounding and verification on the local KG. A hierarchical controller and a privacy-aware experience memory further reduce unnecessary exploration and remote interactions. Comprehensive experiments on six benchmarks show that PrivGemo achieves overall state-of-the-art results, outperforming the strongest baseline by up to 17.1%. Furthermore, PrivGemo enables smaller models (e.g., Qwen3-4B) to achieve reasoning performance comparable to that of GPT-4-Turbo.