These three helpful characters take care of Grandmamma when she's sick with pneumonia. More notably, though, they take care of our narrator. The Nurse and Mrs Spring move in to help care for Grandmamma, but end up tending to her grandson, looking after him, and even cooking his meals (5.15). The Doctor, too, pays extra attention to the narrator. He explains to him what's wrong with his grandma (5.13) and is generally a kind fellow.
What we notice here, though, is that no matter how nice and "jolly" these characters are, they just aren't enough. Simply taking care of our narrator can't earn his love. So what can? Well, we'll let our narrator answer that for himself. In regards to Mrs Spring, our narrator says, "I liked her very much, but she wasn't a patch on my grandmother for telling stories" (5.15). Of course our narrator appreciates the care and concern his grandma shows him, but he's much more invested in her stories – as a seven-year-old would be.
In addition to their relationship with our narrator, these characters also highlight Grandmamma's adventurous spirit. She has grand plans to take her son on a trip to Norway and it's these three characters who won't allow it because of her health. They also try to get her to stop smoking cigars, although that's some advice she sure doesn't follow. By pointing out what it is that Grandmamma shouldn't do, we are able to more clearly see how much she does do, especially considering she's over three-quarters of a century old.