One recap summarizes how the episode begins:
Sarah meets a suspicious nurse at the sleep clinic who she believes is doing harm to the other patients, such as her roommate Dana, who shares some of Sarah's past bad habits. Here is where the dreamcatcher appears, apparently made by a janitor named Hector with a technological coyote tattoo on the back of his neck. Is he possibly part Native? Is he the Trickster Coyote trying the subtly help Sarah cope with her situation?
Hector the "coyote" doesn't do much more than his one scene, in which he explains about the dreamcatcher and his tattoo. So again the Native influence is subtle. But looking at the whole season, it seems the writers are trying to give Terminator a mystical Native vibe.
Previous Native references in the show:
Native souls in Terminator
Cabeza de Vaca in Terminator
Modoc War in Terminator
For more on the subject, see TV Shows Featuring Indians.
P.S. The second summary was written by Beth Aileen Lameman (Anishinaabe, Metis, Irish), who co-created the webcomics THE WEST WAS LOST and FALA. I guess she'd know more about Coyote than most reviewers. Interesting to see another connection between Natives, comics, and television.