When Cecilia breaks her strand of pearls part of the loop remains intact around her neck, but disappears when the camera angle changes.
Julio agrees to do Cecilia's bidding because she threatens to withdraw her statement to the police in which she claimed she did not spot the murderer in the lineup. It is already a stretch that one witness could lead to an accused's conviction, or that Julio did not think to try to provide proof of knowing Cecilia before the murder, as her statement relies on the lie that Julio is a stranger to her.
But one can also see easy stratagems for Julio. First, he might not need proof of knowing Cecilia if he told Agent Ayala about the blackmail, and the prediction that Cecilia would recant her statement. When, lo and behold, Cecilia came to the police to re-accuse Julio, Ayala would be quite suspicious. Or, he could arrange to have Ayala come to the hotel and simply observe Julio and Cecilia talking together, which would make clear they weren't strangers, and would muddy the waters if she later pretended to want a second look at the lineup. The writers tried to get off easy by making Cecilia's blackmail so paper-thin.
But one can also see easy stratagems for Julio. First, he might not need proof of knowing Cecilia if he told Agent Ayala about the blackmail, and the prediction that Cecilia would recant her statement. When, lo and behold, Cecilia came to the police to re-accuse Julio, Ayala would be quite suspicious. Or, he could arrange to have Ayala come to the hotel and simply observe Julio and Cecilia talking together, which would make clear they weren't strangers, and would muddy the waters if she later pretended to want a second look at the lineup. The writers tried to get off easy by making Cecilia's blackmail so paper-thin.