Text Image Machine Translation (TIMT) aims to translate texts embedded within an image into another language. Current TIMT studies primarily focus on providing translations for all the text within an image, while neglecting to provide bounding boxes and covering limited scenarios. In this work, we extend traditional TIMT into position-aware TIMT (PATIMT), aiming to support fine-grained and layoutpreserving translation, which holds great practical value but remains largely unexplored. This task comprises two key sub-tasks: regionspecific translation and full-image translation with grounding. To support existing models on PATIMT and conduct fair evaluation, we construct the PATIMT benchmark (PATIMTBench), which consists of 10 diverse real-world scenarios. Specifically, we introduce an Adaptive Image OCR Refinement Pipeline, which adaptively selects appropriate OCR tools based on scenario and refines the results of text-rich images. To ensure evaluation reliability, we further construct a test set, which contains 1,200 high-quality instances manually annotated and reviewed by human experts. After fine-tuning on our data, compact Large Vision-Language Models (LVLMs) achieve state-of-the-art performance on both sub-tasks. Experimental results also highlight the scalability and generalizability of our training data