According to the newspaper, the 53-year-old argued with police guarding the palace gates before handing over a letter for her sibling.
It's clear to see that there are a number of unresolved issues between them and with reports that Samantha is working on a book about this very subject, Meghan's relationship with her family is sure to be in the headlines for a while yet.
The controversial sister of the newest member of the British royal family has conducted a string of interviews in the months leading up to and following the royal wedding of Meghan Markle to Prince Harry, where she has both attacked the couple, and apologised for her conduct before and after their big day. She made her way about the city in a wheelchair due to multiple sclerosis.
According to the Mirror, Markle had given palace officials an "ultimatum" in which she said she would show up to confront her sister if they did not arrange a meeting.
But her attempts to meet the Duchess of Sussex face-to-face were stalled when a security guard refusing to let her pass.
As Nicki Swift previously reported, Samantha publicly apologized to Markle, 37, last week after flying to London to try to speak with her in person.
A few days ago, Samantha issued a public apology to Meghan on TV.
Grant alluded to her reasons for writing to Meghan, replying in the comments of the tweet, "The Family spoke out about being treated unjustly by her. So moving forward, I apologize and wish things could be different". One source said: "It really hit home for her just how loved Meghan and Harry are".