We investigate the effect of terminology injection for terminology-constrained translation in a low-resource language variety, with a particular focus on off-the-shelf instruction-tuned Large Language Models (LLMs). We compare a total of 9 models: 4 instruction-tuned LLMs from the Tower and EuroLLM suites, which have been specifically trained for translation-related tasks; 2 generic open-weight LLMs (LLaMA-8B and Mistral-7B); 3 Neural Machine Translation (NMT) systems (an adapted version of MarianMT and ModernMT with and without the glossary function). To this end, we release LegISTyr, a manually curated test set of 2,000 Italian sentences from the legal domain, paired with source Italian terms and target terms in the South Tyrolean standard variety of German. We select only real-world sources and design constraints on length, syntactic clarity, and referential coherence to ensure high quality. LegISTyr includes a homonym subset, which challenges systems on the selection of the correct homonym where sense disambiguation is deducible from the context. Results show that while generic LLMs achieve the highest raw term insertion rates (approximately 64%), translation-specialized LLMs deliver superior fluency (∆ COMET up to 0.04), reduce incorrect homonym selection by half, and generate more controllable output. We posit that models trained on translation-related data are better able to focus on source-side information, producing more coherent translations.