Deep neural networks (DNNs) deployed in a cloud often allow users to query models via the APIs. However, these APIs expose the models to model extraction attacks (MEAs). In this attack, the attacker attempts to duplicate the target model by abusing the responses from the API. Backdoor-based DNN watermarking is known as a promising defense against MEAs, wherein the defender injects a backdoor into extracted models via API responses. The backdoor is used as a watermark of the model; if a suspicious model has the watermark (i.e., backdoor), it is verified as an extracted model. This work focuses on object detection (OD) models. Existing backdoor attacks on OD models are not applicable for model watermarking as the defense against MEAs on a realistic threat model. Our proposed approach involves inserting a backdoor into extracted models via APIs by stealthily modifying the bounding-boxes (BBs) of objects detected in queries while keeping the OD capability. In our experiments on three OD datasets, the proposed approach succeeded in identifying the extracted models with 100% accuracy in a wide variety of experimental scenarios.