This paper addresses the challenge of accurately translating technical terms, which are crucial for clear communication in specialized fields. We introduce the Parenthetical Terminology Translation (PTT) task, designed to mitigate potential inaccuracies by displaying the original term in parentheses alongside its translation. To implement this approach, we generated a representative PTT dataset using a collaborative approach with large language models and applied knowledge distillation to fine-tune traditional Neural Machine Translation (NMT) models and small-sized Large Language Models (sLMs). Additionally, we developed a novel evaluation metric to assess both overall translation accuracy and the correct parenthetical presentation of terms. Our findings indicate that sLMs did not consistently outperform NMT models, with fine-tuning proving more effective than few-shot prompting, particularly in models with continued pre-training in the target language. These insights contribute to the advancement of more reliable terminology translation methodologies.