In The Shadow Lines, the narrator's grandmother Tha'mma is a tough, no-nonsense lady, just the kind of person we'd expect to have been a headmistress of a school. Tha'mma has very high standards, by which she judges those around her.
In particular, Tha'mma is a real stickler when it comes to not wasting time. That's why she doesn't want the narrator hanging out with his uncle Tridib. In her opinion, Tridib is nothing but a loafer, a man who wastes his time.
This is about the worst insult that Tha'mma can level at anyone. The narrator's grandmother illustrates her point with a bizarre simile. Apparently, time is like a toothbrush; if it isn't used, then it goes moldy.
The narrator asks his grandmother what happens to wasted time. She responds by saying that it begins to stink, in much the same way, one might think, that an unused, moldy old toothbrush would.
As the narrator reflects, no one's time in his household is ever given “the slightest opportunity to grow moldy.” His grandmother is busy at her job as a schoolmistress; his father is busy at his as a junior executive in a company dealing in vulcanized rubber; his mother is preoccupied with housework. As for the narrator himself, he has plenty of homework to do.