As the use of machine translation (MT) continues to grow, along with the increasing societal demand for inclusivity, research on gender bias in MT is expanding. Gender bias becomes particularly pronounced when translating from a notional gender language, like English, where gender is not always defined, into a grammatical gender language, like Greek, where gender is deeply morphologically embedded. This research proposal focuses on gender fairness in MT for English-to-Greek translations, a highly understudied language pair, and will explore the task of rewriting as a gender bias mitigation strategy. The goal is to develop a human-centered, transformer-based gender-aware rewriter that detects gender ambiguity in the English text and, if present, generates gender-explicit and gender-fair (i.e. gender-inclusive and gender-neutral) Greek translation variants. Designed as a plug-in for integration into existing translation systems (e.g. Google Translate, DeepL), the rewriter will inform users about the presence of gender ambiguity and allow them to select their preferred output in gender-ambiguous cases. The development of gender-fair strategies will be informed by an in-depth investigation of current Greek linguistic practices, resulting in a set of guidelines that go beyond the gender binary in existing (official) guides.