Addressing the challenges in remote music education-such as the complex sources of sheet music images, significant variations in image quality, the heavy burden of manual identification on teachers, and the difficulty of directly applying recognition results to teaching-this paper focuses on the structural restoration of low-quality classroom sheet music images and the generation of instructional prompts. This paper at first builds a music score data arrangement plan which is specially made for remote teaching situations, it unites publicly obtainable OMR data together with screenshots, mobile telephone pictures, classroom video frames, and teacher-marked manuscripts under one single training and evaluation frame. This hereby constructs the RemoteScore-Teach data object, which has the integration of symbol-level annotations, MusicXML alignment outcomes, and bar-level teaching-oriented labels. Building on this foundation, we propose the STG-OMR model, which integrates visual encoding, positional embedding, scale embedding, symbol relationship modeling, sequence decoding, and instructional hint generation into a single recognition pipeline. This enables the system to simultaneously output structured musical score results and bar-level instructional hints. Experimental results demonstrate that the proposed method achieves superior performance on both public benchmarks and remote teaching test sets, with Symbol F1, SeqAcc, and Hint-P may attain 95.4%, 91.7%, and 89.3% upon RemoteScore-Teach, respectively, and it displays higher stability in the situations which include photographed scores, reflective screen captures and annotated scores. The cutting experiments further prove that the score position prior information, the relation graph restriction conditions and the teaching hint branch structure are the main sources that bring performance promotion. This research provides practical technical support for pre-class preparation, in-class identification of key measures, and post-class assignment screening, while also offering a new implementation path for intelligent score analysis in remote music education.