For example in a story I'm writing a character says the following:
“Be careful,” An-Mei said, ignoring my question. “No matter what, don't get close to her.”
Later on the protagonist thinks about this:
I had decided to avoid the mountain at night. Be careful. Don't get close to her, An-Mei had said. But did why people fear her so much?
Should I italicize Be careful. Don't get close to her?
I'm not sure it's necessary.
Some authors use this technique when not crediting the person who said it. This technique works best when the 'narrator' quotes it multiple times.
I had decided to avoid the mountain at night. Be careful. Don't get close to her. But did why people fear her so much?
In your example, you're crediting the person who said it, which is a direct reference to the original scene/person. You don't need to italicise.
I don't think there's a hard-and-fast rule to this, but I think italicising and crediting may be too much.
Your decision also has to take into account how long ago the quote occurred. If it's too many scenes back, then you risk the user not knowing where it came from.
I think italics would be perfect. It makes total sense that the protagonist is recalling what someone else said — it's sort of an in-line flashback. Otherwise, how are you going to indicate that it's remembered dialogue? Quote marks make it look like An-Mei is there, speaking, when she's not, and a lack of any marking looks like a mistake.
You can leave in the credit or not; I generally like to err on the side of clarity, and I think here it reads fine to leave it in.
