Zero-shot depth completion with metric scales poses significant challenges, primarily due to performance limitations such as domain specificity and sensor characteristics. One recent emerging solution is to integrate monocular depth foundation models into depth completion frameworks, yet these efforts still face issues with suboptimal performance and often require further adaptation to the target task. Surprisingly, we find that a simple test-time training, which fine-tunes monocular depth foundation models on sparse depth measurements from sensors just as it is, yields reasonable results. However, this test-time training obviously incurs high computational costs and introduces biases towards specific conditions, making it impractical for real-world scenarios. In this paper, we introduce a new approach toward parameter-efficient zero-shot depth completion. Our key idea of this work is to leverage visual prompt tuning, achieving sensor-specific depth scale adaptation without forgetting foundational knowledge. Experimental results on diverse datasets demonstrate that our approach outperforms relevant state-of-the-art methods, showing superior generalization and efficiency. Our source code is available in the supplementary materials.