How does the nuance of this sentence change if I change "an idea" to "the idea"?
Answer from a Native speaker
Using "the idea" instead of "an idea" actually makes the word "idea" more specific. "A, an, the" are all considered articles. "A" and "an" are considered indefinite articles, meaning that they help to generalize non-specific nouns. "The" is considered a definite article, meaning that it specifies nouns. The two men are telling Emma Watson's character that they have an idea; an idea that she knows nothing about and that these men have not gone into detail about. Since they did not discuss what the idea is yet, it should not have the definite article "the" before it. Here are examples of "a/an" being used. Ex: He has a dog. Ex: We live in an apartment. Ex: I have a cat. Here are examples of "the" being used. Ex: Could you please grab the keys? Ex: We want the car in garage. Ex: I need the cake in the oven before noon.