The Quiet Man

Sean and Mary Kate
In the 1920s, Sean Thornton (John Wayne), an Irish-born American from Pittsburgh, travels to Ireland to reclaim his family's farm and his birthplace in Inisfree. He meets and falls in love with the fiery Mary Kate Danaher (Maureen O'Hara), the sister of the bullying, loud-mouthed landowner Squire "Red" Will Danaher (Victor McLaglen). Danaher, who had wanted the farm himself, is angry that the Widow Tillane (herself angered by Danaher's admission that he had discussed her in the local pub) accepts Sean's bid, and retaliates by refusing consent for his sister to marry. Several town locals, including the Catholic priest, Father Lonergan (Ward Bond), conspire to trick him into believing that the wealthy Widow Tillane (Mildred Natwick) wants to marry him, but only if Mary Kate is no longer living in his house. After learning the truth on Sean and Mary Kate's wedding day, an enraged Will refuses to give his sister her dowry which is made up of a large sum of money and her family possessions passed down from her mother.
Sean, unschooled in Irish customs, cares nothing about the dowry, but to Mary Kate the dowry represents her independence, identity, and pride. She feels passionately and intensely that the dowry is hers and is needed to validate her marriage to Sean. Angered and shamed by Sean's refusal to confront her brother and demand what is legally hers, she brands him a coward, and, despite living together, they are quickly estranged as husband and wife. In the morning they find that others in the village had visited Will and pressured him to return Mary Kate's furniture, but not her money.
Sean had been a boxer in the United States, a heavyweight challenger known as "Trooper Thorn". After accidentally killing an opponent in the ring, Sean hung up his gloves, vowing never to fight again. This is known to only one person in the village, the Church of Ireland minister, the Rev. Playfair (Arthur Shields), who once upon a time had been the lightweight champion and so understands Thornton's internal conflict over the fight.




Scene from the film
In an attempt to force Sean to confront Will, Mary Kate leaves him and boards a train departing Castletown and headed to Dublin. Sean hears that she left for the station and drags her off the train. Followed by the crowding townspeople, he forces her to walk with him the five miles back to Inisfree and directly to the Danaher farm. Sean demands that Will hand over her dowry. When Will refuses, he throws Mary Kate back at Will, saying that "no dowry, no marriage" is their custom not his, shocking the two and shaming Will into finally paying the monetary part of his sister's dowry. Sean promptly throws the money into a nearby furnace which Mary Kate holds open, showing that Mary Kate never cared about the money, but only what it represented.
After a proud Mary Kate announces so all can hear, that she will now return home to prepare his supper, and departs, Will punches Sean, and a long, memorable fistfight ensues between the two, drawing crowds from miles around. They slug it out through the village, stop for a drink, brawl again, then, somewhat drunk, admit grudging mutual respect and the two return to Sean and Mary Kate's home for supper, where it is implied the rift is healed. Sean regains Mary Kate's love and respect. In the aftermath it is shown that Will and the Widow Tillane begin courting, and "peace is returned to Inisfree".

Question: What happens between Will and the Widow Tillane at the end of this scene?
Answer: Begin courting