The king proposes a wager with Queen Katherine, his archers against any she may choose. She sends for Robin and his men, giving them false names. They win and are revealed but the king has promised not to be angry with any in the queen's party.
There is no historical "Queen Katherine"; the wife of King Stephen (1135-1154) was Matilda; the wife of Henry II (1154-1189, the first king usually associated with Robin Hood) was Eleanor of Aquitaine; Richard I (1189-1199) married Berengeria of Navarre; John (1199-1216) has as his primary wife Isabella of Angouleme; Henry III (1216-1272) married Eleanor of Provence; Edward I (1272-1307) married first Eleanor of Castile and then Margaret. By this time the longbow was established, and Robin Hood's exploits with the bow would no longer have been noteworthy. Leach speculates that one of Henry VIII's wives (either Catherine of Aragon or Catherine Howard) is meant!
The sequel to this story is told in Child 146, "Robin Hood's Chase."
For background on the Robin Hood legend, see the notes on "A Gest of Robyn Hode" [Child 117]. - RBW