Open-set object detection (OSOD) localizes objects while identifying and rejecting unknown classes at inference. While recent OSOD models perform well on benchmarks, their behavior under realistic user prompting remains underexplored. In interactive XR settings, user-generated prompts are often ambiguous, underspecified, or overly detailed. To study prompt-conditioned robustness, we evaluate two OSOD models, GroundingDINO and YOLO-E, on real-world XR images and simulate diverse user prompting behaviors using vision-language models. We consider four prompt types: standard, underdetailed, overdetailed, and pragmatically ambiguous, and examine the impact of two enhancement strategies on these prompts. Results show that both models exhibit stable performance under underdetailed and standard prompts, while they suffer degradation under ambiguous prompts. Overdetailed prompts primarily affect GroundingDINO. Prompt enhancement substantially improves robustness under ambiguity, yielding gains exceeding 55% mIoU and 41% average confidence. Based on the findings, we propose several prompting strategies and prompt enhancement methods for OSOD models in XR environments.