We present WinoTR, a Turkish adaptation of the WinoMT challenge dataset (Stanovsky et al., 2019). While WinoMT has been widely studied across multiple languages, its adaptation to Turkish — a morphologically rich language with no grammatical gender — and its analysis through a causal lens remain unexplored. Using 4,752 sentences adapted from the original dataset across pro-stereotypical, anti-stereotypical, and neutral conditions, we apply Double Machine Learning (DML) to estimate the causal effect of gender cues on stereotype-consistent translation output. Our results reveal a striking asymmetry: cue direction has a large and statistically significant effect on translation outcomes, while cue presence alone produces virtually no effect. Even without any gender signal, MT systems default to stereotype-consistent translations in 62.9% of cases across three systems (DeepL, Google Translate, OpenAI). By leveraging this typological property, our causal analysis reveals that gender bias in contemporary MT and LLM-based translation systems runs deeper than surface-level cue processing, persisting as an embedded prior independent of any explicit gender signal in the input.