When Picard does a double-take on Sito, he's noting, "She's a Bajoran..." You can tell this is when Picard realizes a possible solution to his problem. When he takes her with him after visiting the Cardassian in sick bay, he asks if she's a pilot. When she confirms it, that's another step to confirming the viability of his plan. He then dresses her down to test her mental strength. When she comes back and defends herself, she completes his test for his Xanatos Speed Chess.
Worf knew Picard asked for Sito to serve on the Enterprise as a second chance for her past crime. He probably also knew Picard had dressed her down for that crime, and knew it was a Secret Test of Character. He was actually cheating by giving Sito broad hints to confront Picard about treating her unfairly.
Sito is not wearing a ceremonial Bajoran earring. Ensign Ro's example showed that they are, at least at this point in the franchise, against Starfleet dress code, and Ro was only able to wear one by leveraging a favor from Picard in her first episode. Sito, living in the shadow of her academy disgrace, has not earned anyone's permission to bend the rules.
Considering she didn't wear one at the academy even when she had a perfect record it's also just as likely she never considered to ask for special permission. A lack of self confidence and speaking up for herself was a big character flaw of hers, it's why she went ahead with listening to Locarno and why Worf had to give her a special lesson is speaking up for herself.
Consider the Red Shirt phenomenon in Trek circles, and then think of how often Picard, and Kirk before him, has had to make that announcement at the end. Think of how many social circles can form on ships of hundreds of people, who have to go through what the group in this episode goes through.
