Teeter's backstory on "Yellowstone" is that she hails from Texas. It's unclear what area of Texas she's from, and that ambiguity is likely intentional. It's not a common accent and is probably more grounded in what a Hollywood writer believes someone from the Texas boonies would sound like. But ultimately, it's that way of speaking that makes her such an interesting character.
She's pretty much the sole woman around the bunkhouse, but she's not intimidated by the other men. She spews profanities with the best of them and hits on some of her co-workers, trying to get them to give her a back rub (or, as she would call it, a "bekkrewb"). The Teeter accent shows she came from a rough, rugged upbringing. She's not some city slicker trying to ride horses; she embodies the country spirit. There's also depth to Teeter, as she showed off a more vulnerable side in a "Yellowstone" scene that went too far where she had to beg John Dutton (Kevin Costner) to let her keep her job.
It's a testament to Jennifer Landon's acting ability that she embodies the character so well. Landon, the child of actor Michael Landon, was born in Malibu, California, and then pursued a degree at New York University. It's a far cry from Teeter's rural roots, but Landon must've had a good dialect coach at some point.
