While they walk around the house, Milly tells Lord Mark that she tends not to go out on the Italian streets anymore. He asks if this is because she's ill, but she doesn't give a straight answer.
Instead, she looks out a window and drops her face onto her arms. She almost wants to cry after hearing Lord Mark ask about her health.
At this moment, Milly has a revelation. She realizes that her terrible health might actually be a point of attraction for any man hoping to marry her. If she dies, after all, the man will get all of her money. She seems not to have realized this before: Milly basically has a bright, blinking "innocent" sign above her head.
Lord Mark starts tiptoeing around the idea of them getting hitched, asking if Milly would ever be able to see herself loving him.
Milly doesn't bite. Pro-tip: don't try to hit on a dying girl with the pick-up line "Soooo… you're dying, huh?"
Lord Mark says that he thinks Milly is in love with someone else. She reacts to this defensively by saying that she definitely doesn't want him. Burn. Milly also says that Lord Mark should be ashamed, since it's Kate whom he's supposed to be going after.
Lord Mark says that he can't be with Kate because Merton is in love with her. Milly admits this is true, but claims that Kate doesn't love Merton back. Lord Mark really messes everything up by saying that he is positive Kate returns Merton's affection and that the two are in love.
This shakes Milly up, but she continues to insist that it's not true.
While they argue, Lord Mark suddenly asks why Milly is suddenly so interested in whether Merton and Kate are in love. He seems to recognize the emotional stake she has in it.
At this moment, a servant comes in and announces that another guest is waiting. Milly asks who it is, and in front of Lord Mark, the servant says that it's Merton Densher. At this, Lord Mark truly seems to realize what's going on.