We propose a collaborative edge-to-server inference framework for vision-language models (VLMs) that reduces communication cost while maintaining inference accuracy. In typical deployments, visual data captured at edge devices (clients) is transmitted to the server for VLM inference. However, transmitting full-resolution images incurs high communication cost. Conversely, aggressive downsizing or excessive compression to mitigate communication overhead can discard fine-grained details, leading to accuracy degradation. To overcome this limitation, we design a communication-efficient two-stage framework. In the first stage, the server performs inference on the downsized thumbnail (global image) and quantifies the min-entropy of the output tokens. If the min-entropy exceeds a predefined threshold, the server identifies a region of interest (RoI) using the VLM's internal attention and requests the edge device to send a detail-preserved local image of the RoI. The server then refines its inference by jointly leveraging the global and local images. This selective retransmission strategy ensures that only essential visual content is additionally transmitted. Experimental results consistently confirm that the proposed framework substantially reduces communication overhead while maintaining inference accuracy across diverse VQA benchmarks.