I am unsure what this could be. Originally, I thought the first lady was going for the weed flowers, which I have seen sold in the stores. However, it appeared to be more than just the flowers. And the other folks didn't look to be harvesting flowers...but they were harvesting something growing in the grass on the public land!
In a brief internet search, my attempt at explaining this is: Naengi, or Shepherd's Purse.
From an official website: "Naengi, with its unique smell, is the most beloved of Korea’s wild spring vegetables. Naengi is not broken down when boiled in water and is rich in protein, calcium, iron, and minerals. This wild vegetable contains so much vitamin A that just eating 100g of it constitutes a third of the daily requirement.
"According to oriental medicine practitioners, naengi is good for the health of the stomach and intestines, and helps the kidneys to remove toxic substances. Naengi’s roots improve the health of the eyes and are also said to be good for women who have just given birth since they contract the womb and reduce swelling."
http://english.visitkorea.or.kr/enu/SI/SI_EN_3_6.jsp?cid=713941
*None of these photos are mine. They are from a web search on the particular plant.*
