A promising paradigm for adapting instruction-tuned language models is to learn task-specific updates on a pretrained base model and subsequently merge them into the instruction-tuned model. However, existing approaches typically treat the instruction-tuned model as a passive target that is only involved at the final merging stage, without guiding the training process. We propose GIFT (Guided Fine-Tuning and Transfer), a simple and efficient framework that incorporates guidance from the instruction model into task adaptation. GIFT fine-tunes a low-rank adapter on the pretrained base model using confidence signals derived from the instruction-tuned model. The learned adapter is then merged into the instruction-tuned model, yielding task-specialized models that preserve general instruction-following behavior. We evaluate GIFT on mathematical and knowledge-intensive benchmarks across multiple model families and scales. Results show that GIFT consistently outperforms direct fine-tuning and representative transfer-based baselines, while maintaining robust generalization and favorable test-time scaling behavior.