I cannot seem to find anything on the matter but have seen entries on multiple K for P lists about mustard being forbidden.
והמנהג שלא לאכול חרדל כלל בפסח ... דהוי כמיני קטניות שנוהגין בו איסור:
The custom is not to eat mustard at all on Pesach ... because it is like kitniyot (legumes) which we are accustomed to prohibit.
Mishnah Berurah 464:5 quotes from Levush that this is because mustard seeds are harvested and gathered like grains.
Mustard is not forbidden on Passover. Ashkenazi Jews from Europe have a custom to not eat "kitniyot," which is commonly translated as legumes. And as part of this custom they have decided that mustard is a legume. Therefore it's not actually prohibited, but Kashrut agencies do their best to adhere to the very large Ashkenazi custom of prohibiting kitniyot and so they will often list mustard and other kitniyot products as forbidden.
Jews of Sephardic, Ethiopian, Yemenite, and other Jewish heritages from the middle east all eat mustard on Passover, along with most other types of Kitniyot. So it's important to distinguish what is actually forbidden from "a custom of refraining," because otherwise someone might see a Sephardic Jew eating mustard and think the Sephardic Jew is sinning by eating a prohibited food.