The use of gender-fair language can lead to a more inclusive society, yet machine translation (MT) systems frequently reproduce and amplify gender bias. Some of this bias is due to inherent ambiguities in the source: English largely lacks grammatical gender marking, whereas Greek requires morphological and semantic gender specifications, forcing MT systems to resolve ambiguity in ways that default to gendered (and often biased) outputs. This research explores gender-fair rewriting as a strategy for bias mitigation for English-to-Greek MT, a language pair that remains highly understudied. We propose a twofold approach: ReGender, a system that first detects gender ambiguity in the English source text and then generates a set of gender-fair Greek translations for the ambiguous cases, including gendered, gender-neutral, and gender-inclusive forms. Through a human-centered design, the project combines NLP methods with community-informed gender-fair language practices that go beyond the gender binary. The resulting model will take the form of a plug-in that can be integrated into existing MT systems, enabling users to make informed translation choices while promoting the broader goal of inclusive language technologies.