Kay undoubtedly read about the Sollozzo/McCluskey murders in the newspapers, just like millions of other readers. She might have connected Michael's sudden and unexplained disappearance to the murders, though I doubt it, given her (later) tendency to deny or overlook Michael's worst aspects.
You can explain Tom's reaction to Kay by imagining what happened right after the murder. Police called to the scene would have made a connection between the shootings and McCluskey breaking Michael's jaw (he did it in public, in front of a bunch of cops, at least some of whom would be at the restaurant to help track down the murderer of their boss). They'd have circulated a description, photo or drawing of Michael, and at that point, at least some of the witnesses would have helped them. But when they came looking for Michael at the Mall, Tom would have met them and told them that Michael had departed for parts unknown before the shooting. The police may even have put out an APB on Michael, or gotten a judge to issue a bench warrant for his arrest.
So, when Kay arrived with a letter for Michael, Tom had no idea what was in the letter--could she have said, "I know you did it but I still love you?" He didn't know if she was pissed at Michael for dumping her without explanation, and may have been working with the cops to set up Tom. She might have been wearing a wire, or could have been watched by the cops. So, his safest course of action--the only one, really--was to refuse to accept the letter.