ITE scores are surrogate markers of whether you're at risk of failing your boards. Accredited fellowships hate it when you don't get board certified as it dings their metrics.
Still, that one score is a tiny part of the review process. While it may gate you out of some fellowships, almost no one would care about an isolated low test score. If they ask, you were on a horrible ICU rotation, covering night call at 2 hospitals, and your pet died.