Korra bade her parents farewell before she embarked on her voyage to the city. They were supportive of their young daughter, enough so to let her travel to Republic City and follow her destiny.
They discovered she was the Avatar when Korra began bending water, earth, and fire at only four years old. Korra's parents are caring and understanding of their daughter, and she seems to have a good relationship with them. Korra embraced her parents, Tonraq and Senna, before her departure from the Southern Water Tribe.
'We love you so much.' ― Korra saying goodbye to her parents.