It begins automatically at some point after bringing Marlene to safety at Corvo Bianco. The quest seems to be triggered by being off of Corvo Bianco grounds (or leaving them, if you meditated/slept on the grounds) after Marlene has been there for an in-game day or two.
On your way there, you can just fast-travel to Trastamara Estate Ruins, and you shouldn't encounter any monsters/enemies.
Marlene's dowry is in the lower room with the nightmare-level of spoon hoarding (the one where the entire floor is covered in spoons). The dowry is placed in 2nd-most barrel from the right-most barrel (from the perspective as you enter the room).
- The witcher had decided not to kill the wight. A fortunate decision, as the monster had proved to be a woman named Marlene, afflicted some time past by a terrible curse. The witcher had lifted the curse and learned Marlene's story. She had suffered unimaginable pain while cursed, fated forever to hunger and waste away. Geralt, big-hearted as he was, could not leave the woman to fend for herself. He invited her to stay at Corvo Bianco, the estate the duchess had granted him in recognition of his service. The estate's majordomo took Marlene under his wing. The witcher decided he would visit the cured woman several days later.
- Geralt encourages Marlene to live a new life in town:
- Geralt had proven a generous soul when he let Marlene recover at Corvo Bianco. After a time, they had a candid conversation, and the woman revealed her concerns. With the curse having held her for centuries, she had outlived her loved ones and was now left with no one to turn to. Time had passed, the world had progressed, and Marlene felt like a stranger within it. The witcher believed only living among other folk could restore the balance Marlene had lost. Marlene agreed and a few days later their paths diverged as she set off to make a new life for herself.
- Geralt offers Marlene to stay at the estate:
- Marlene turned out to be an open and honest woman. She and Geralt had a friendly, candid conversation and decided she would remain at Corvo Bianco for the foreseeable future. She would tend to the kitchen there. Thus, in addition to Marlene's gratitude, Geralt gained an able cook (the majordomo was thought to have no culinary talents whatever, having burned several pots of water in his time). Marlene also told the witcher that a long time past her father had amassed for her a dowry that was likely to be lying undisturbed in the cellars of the Trastamara Estate.