Speaking to United Kingdom tabloid the Mirror, a source said the latest development "spoke volumes".
The source told the Mirror: "This is the closest Meghan has come physically to that side of her family since she married into the royal family but palace staff had clearly been instructed not to allow her access".
Samantha Markle, the outspoken half-sister of Meghan, was reportedly turned away from the Duchess's doorstep after arriving uninvited. "She told them that she had discussed with officials of the palace".
Samantha has maintained that she went public with her feelings towards Meghan because she feels her father, Thomas Markle, deserves respect and that he shouldn't have been isolated.
Samantha, who is confined to a wheelchair due to multiple sclerosis, was accompanied by her partner. "It was a sad sight".
Samantha added that her step-mother Doria Ragland was made to look like the better parent.
When asked to tell more about the letter, Meghan's sister said in part that 'I can not tell you what I wrote but I think that I accomplished my goal and we will just have to wait and see how it was received.
As fans of the royal family may already know, Meghan Markle's estranged relationship with Samantha and their father, Thomas Markle, has been well-documented in the press. She added, "Moving forward, I apologize and I wish things could be different".
Although not invited to Kensington Palace, Markle showed up unannounced, with photos showing the exact moment that she was turned away, though Markle still said it was a "wonderful experience".
She warned her behaviour would "escalate" if her attempts were ignored by the royal family.