Greg Baylor was a serial killer, an accomplice of Owen McGregor, and a member of a group of corrupt Sheriff's Deputies. He first appeared in Season Nine of Criminal Minds.
After being personally unable to kill Spencer Reid, who witnessed him flee during a shootout between the authorities and Christian preacher Justin Mills (whom the Deputies intended to frame for a series of murders the Deputies were committing), Owen McGregor orders Baylor to go undercover as a nurse and kill the agent. Baylor tries to do so by injecting carbenicillin into Reid's IV, but the latter objected, citing that he had a "bad reaction" to it.
When Baylor refused to listen, Reid slapped the syringe out of his hand, to which he then tried to shoot him with a gun. However, Penelope Garcia, who was overseeing the entire thing, pulled out Reid's revolver from an items bag and shot Baylor before he could pull the trigger. He is then treated for his gunshot wound and incarcerated.
Baylor reappeared in the episode, where it is revealed that he was sentenced to death due to numerous murders he committed and was waiting on death row. When Garcia, guilty for shooting him and therefore landing him on death row in the first place (she had never supported the death penalty), sends him a letter, he intentionally ignores it.
She then visits Texas to see him in prison, and he initially ignores her. However, after no one else comes to visit him, Baylor calls Garcia and tells her to come over and visit him. When she does, she immediately begins apologizing for what she had done, but he shoots her down. Garcia then deduces from details of their conversation that she was his only visitor, to which Baylor tells her that she is right and requests that she be there during his execution, since she was the only one who ever cared for him in his life. Conflicted, Garcia tries calling Derek Morgan for advice, but due to a spat between them regarding her visit to Texas, he doesn't respond.
Eventually, Garcia indeed goes to watch his execution, and Baylor spots her among the other observers. When asked if he has any last words, he says "Thank you" to Garcia before dying of lethal injection.