LANE: My mother and father are sending me to Korea for the summer to visit my cousins.
LANE: They’re sending me to Korea and they won’t tell me when I’m coming back.
Mr and Mrs Kim have bought Lane a one-way ticket to (South) Korea for the summer, leading her to panic they never intend for her to come home. This story line was based on an incident from the childhood of Helen Pai, the real life inspiration for Lane Kim. Her parents did exactly the same thing, but as with Lane’s case, it turned out all right.
The American flag in the background is surely a symbol of where Lane’s heart lies, and also shows that she will return home. In Korea, the colour yellow can be symbolic of good luck, so Rory giving Lane the yellow daisies wishes her good luck on her travels.