She wrote to her mother to give her an excuse to tell Robb she was pregnant, to make her death that more horrific.
As to why Talisa is more invented, it’s more that Talisa exists only to die. Jeyne has a specific backstory that is a significant part of the Red Wedding – she’s a Westerling, which creates a Romeo and Juliet thing b/c she’s a Lannister bannerwoman, her ancient but poor house maximally pisses off Walder Frey, her mother being Sybell Spicer the granddaughter of Maggy the Frog is linked to Tywin’s plotting to trap Robb at the Twins – and significantly, she survives the Red Wedding. There is more to her story than dying at Robb’s side.