The royal couple spent 45 minutes touring the exhibit.
Thomas said he no longer has a working phone number for Meghan. As for the exhibition that coincides with the 100th anniversary of Mandela's birth, she said it was "fabulous" and a "great tribute".
Issues among the newlywed's family have been widely reported and it's not the first time her half-sister has attacked her online.
Meghan was pictured speaking at length with Mandela's granddaughter Zamaswazi Dlamini-Mandela at the exhibition, who praised both her and Harry, saying their stance on "justice and fairness in the world makes them a shining example for the youth of today".
Prince Harry visited Mandela's cell on the island during a 2015 trip to South Africa.
Leading former anti-apartheid campaigner Lord Hain, who is chairman of the Nelson Mandela Centenary Exhibition, said: "London was the centre of the anti-apartheid struggle".
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Taking aim at Meghan, she added: "Glad you have so much time to gallivant around paying tribute to others while ignoring your own father!" Dlamini-Mandela said they don't just talk about doing something, they do it.
The report stated that the exhibition has been divided into six separate themes, including character, leader, comrade, prisoner, negotiator, and statesman. As noted by The Sun, Mandela died at the age of 95 in Johannesburg at his home on December 5, 2013. He was arrested in 1962 for attempting to overthrow the apartheid state and sentenced to life imprisonment.
He received a sentence of life imprisonment but was released in 1990 after 27 years behind bars.
On the decision to stage the exhibition in the capital, the CEO of the Nelson Mandela Foundation, Sello Hatang, said: "London was both South Africa's colonial metropole and the headquarters of the global anti-apartheid struggle".
Mandela and the Queen built up a firm friendship, with South Africa's former president calling her "Lizzie" according to his daughter Zindzi Mandela.