The phrase "true love seeks nothing in return" is meant to suggest that true love is about selfless giving. To me, the story (perhaps inadventently) calls into question what it means to be "selfless."
One can read the story as arguing that such giving is ennobling and redemptive. The entire premise of the story—that Gillian stands to inherit $50,000 if he can "prove" his worth by spending an initial $1,000 wisely—suggests that Gillian has been a selfish spendthrift. His love for Miss Hayden is evidence to the contrary: not only does he tell her (falsely) that the thousand dollars was left to her and give her the money, he does so even though he knows that she does not return his love. When he finds out about the $50,000 he might get because of this selfless act and learns that otherwise the money would go to Miss Hayden, he lies again and tells the lawyers that he lost the money gambling. Not only does he forfeit his inheritance to Hayden, he does it in such a way that she cannot know he was her benefactor. His love for her has caused him to act generously.
A more problematic reading of the story would consider Hayden's position as a dependent woman, her near absence from the story (her only words are "Oh" and "I am sorry"), and the fact that Gillian's redemption is based on deception. It's not too hard to imagine how Hayden would feel had she known what Gillian really was doing—she surely would have rejected the money, since she would not want to be in debt to a man she did not love. In this reading, Gillian's ploy takes Hayden's agency from her and leaves her no say in her fate.
Robert Gillian, the only living relative of a very wealthy man, gives away his inheritance to the woman he loves despite her admission to him that she cannot return his love.
After Young Gillian's uncle dies, he is given $1,000 with instructions that he must spend it, and he must account for how he has spent it. This gift is a test of Robert Gillian's motives. His uncle, who supported his nephew while he was alive, has devised a test with this money, believing he will squander the money. Young Gillian proves him wrong as he gives his $1,000 to Miss Hayden, the ward of Mr. Gillian to whom only $10 and a ring was left; Robert gives this to her despite the fact that his love for her is unrequited. Moreover, when he is about to turn in his envelope with the record of what he has done with his money, he learns that he will inherit $50,000 if he has been altruistic in his expenditure. So, in order that Miss Hayden will also receive this, Gillian tears up his envelope containing the accounting of his charitableness. He tells the lawyers,
"I lost the thousand dollars on the races. Good-day, gentlemen."
Tolman & Sharp are baffled as Gillian is heard whistling happily. Love is its own reward and seeks nothing in return.