For what is this second that-clause placed?

Question

“. . . I’ll bet he killed a man.” She narrowed her eyes and shivered. Lucille shivered. We all turned and looked for Gatsby. It was testimony to the romantic speculation he inspired that there were whispers about him from those who had found little that it was necessary to whisper about in this world.
(F. Scott Fitzgerald, The Great Gatsby)

The first ‘that’ seems to take a role adding information about ‘speculation.’ But I’m wondering for what the second that-clause is placed. Would you let me know?

Answer 1

The second that introduces a relative clause which modifies little. In effect:

It was necessary to whisper about little in this world.

This world is the society is the ‘smart set’, the wealthy would-be sophisticates among whom the novel is set. In saying that they “found little that it was necessary to whisper about”, the narrator implies that they made a point of speaking quite frankly about matters which an older generation spoke about only in whispers. That they did speak about Gatsby in whispers is for that reason remarkable—the “romantic speculation he inspired” involves matters which are unusually scandalous.

Answer 2

You could rephrase it as

...from those who had found little reason that it was necessary to whisper about in this world.

It basically means

...from those who had found that it was unnecessary to whisper about in this world.

So, it was mostly unnecessary to whisper about the romantic speculation he inspired.