Divorced and childless as well as missing a leg, Rayment is perhaps trying to turn his life into a Hollywood screenplay in which a loss is amply compensated by making possible some greater gain. Clint Eastwood's Gran Torino and Victor Nunez's Ulee's Gold come to mind, Rayment being an older man, but examples abound. A kind of secularized theodicy -- yes, there is pain and loss, but in the bigger picture... etc.
However, the nurse and her family do not play along. They appreciate Rayment's gestures, up to a point, but find him a little weird, a little off-putting, and resist being adopted the way he wants to adopt them.
Elizabeth Costello -- a writer/animal rights activist from Coetzee's novel that bears her name -- shows up, invites herself into Rayment's home and life, and tries to talk him out of his deluded project. Her abrupt comings and goings and her mysteriously exact knowledge of Rayment's circumstances lead the reader to think that Rayment is actually a character in a novel Costello is writing. But he is a character with a mind of his own. She wants him to go in a certain direction -- he resists.
The nurse's family's resistance to Rayment's project goes to show that people don't want to be merely characters in someone else's novel -- the Costello vein of the novel goes to show that even characters in novels don't want to be characters in other people's novels. Rayment's resistance to and resentment of Costello should enable him to understand his situation vis-à-vis the nurse's family, and by novel's end, he is perhaps beginning to. Perhaps. As the title indicates, he's not quick.