If you moved out around in the sentence, you can see its function change:
- He pulled out a little scrap of paper from his jeans pocket. (Adverb, linked to the word pull)
- He pulled a little scrap of paper out from his jeans pocket. (You could analyse out as an adverb here, still linked to the word pull, or you could say it's part of a multi-word preposition out from telling us about the position of the scrap of paper)
- He pulled a little scrap of paper from out of his jeans pocket. (Part of a multi-word preposition, telling us about the position of the scrap of paper)
At the end of the day, these all describe the same scene. The difference between them is so subtle that many people would not even notice it.
Is one better than the other? That's a whole other question! You could argue that the word out is redundant in all of these and could be deleted entirely:
- He pulled a little scrap of paper from his jeans pocket.
Problem solved!
But we're not here to talk about the best version of this sentence—we're here to help you realise that sometimes a word you think is a preposition is not acting as a preposition at all (and if you guess that it's an adverb, you're probably right).