Gretchen Hudson was the wife of Calvin Hudson. Both Gretchen and Calvin were close friends of Benjamin Sisko, Jennifer Sisko, and Curzon Dax.
In 2354, Gretchen attended the Mazurka Festival in New Berlin with her husband and the Siskos.
Gretchen Hudson died during Benjamin Sisko's first year in command of Deep Space 9. (DS9: "The Maquis, Part I")