We were all ready to describe Gerty to you in heartbreaking detail, but then we remembered that Wharton does a much better job. Here you go:
Miss Gertrude Farish, in fact, typified the mediocre and the ineffectual. If there were compensating qualities in her wide frank glance and the freshness of her smile, these were qualities which only the sympathetic observer would perceive before noticing that her eyes were of a workaday grey and her lips without haunting curves. (1.8.11)
OK, so she's not attractive, she's not wealthy, and she basically has no social currency. But Gerty also has no aspirations to join the circles of the social elite; she's quite content to live her life on the fringe of social scene, her one connection to it being her cousin Lawrence Selden.
About that – Gerty is in love with her cousin, which apparently was still acceptable in the late 1800s. When she discovers that he's in love with Lily – and in fact has only been spending time with Gerty to talk about his crush – she gets pretty mad. She rages (internally) against the thieving, conniving, man-stealing Lily Bart. We fully expect that, when Lily shows up at her doorstep asking for help, Gerty will leave her out in the streets.
And then… Gerty forgives Lily and takes her in. Which brings us to our next big point in discussing Gertrude's character: she's really nice. Gerty's hobby is philanthropy; she works for a variety of charities and is responsible for the Girls Club where Nettie Struther later reveals she found help. Gerty is unlike any other character in House of Mirth in that she really is a genuinely generous person. Others may engage in charity – like Mrs. Fisher or even Lily – but their motives are far from pure. Look at the way Wharton describes Lily's decision to donate $300 to Gerty's charity:
The satisfaction derived from this act was all that the most ardent moralist could have desired. Lily felt a new interest in herself as a person of charitable instincts. […] Moreover, by some obscure process of logic, she felt that her momentary burst of generosity had justified all previous extravagances, and excused any in which she might subsequently indulge. Miss Farish's surprise and gratitude confirmed this feeling, and Lily parted from her with a sense of self-esteem which she naturally mistook for the fruits of altruism.
Unlike Lily, Gerty's charity work really is selfless in nature. We see examples of her moral fiber over and over again, nowhere more clearly than in Book II when she goes out of her way to help Lily. She's not interested in Lily's financial well-being as much as she is about her moral well-being. She worries that Lily is "cheapening herself" by hanging out with people lower on the social ladder. Because Gerty has helped Lily in the past, she feels she has a "moral claim" on her character: "Having once helped Lily, she must continue to help her; and helping her, must believe in her, because faith is the main-spring of such natures" (2.5.17).
It's no coincidence that the one character with a conscience we have happens to also be a poor woman consumed by "dinginess." Remember when we talked about the antithesis of money and morality in Lily's "Character Analysis"? Gerty is a prime example. No money, but intense moral scruples.