This story is nowhere mentioned in the Vyasa Mahabharata.
However, southern versions like Perundevanar's Bharata Vemba, Pampa's Vikramarjuna Vijaya and Villiputturar's Bharatam do mention this incident.
The only source I found was Mahabharata and Variations Perundevanar, Pampa and Nannayya a Comparative Study(page 49) by Acharya Kambalur Venkatesa, a Shodhaganga research paper, as I don't think the above versions of Mahabharata have ever been translated to English.
Bharata Vemba gives the story thusly:
5A VI - N. KARNA PLAYS A GAME OF DICE WITH DURYODHANA’S QUEEN
Karna explains to Kunti, how such help Duryodhana has done to him.
When he was a man without any identity Duryodhana differed him a
crown, made him the King of a state and respected him more than his
own brothers and many other kings. Duryodhana loved him to such an
extent that he ate-.How can I desert a friend who ate with me with
Finally Karna reveals an incident which speaks volumes of the
confidence and sincere friendship of Duryodhana for Karna.
One day Karna was playing a game of dice with the queen. She lost the game. When she was about to go without paying the stake Karna
caught hold of her sari. The bracelet of the queen gave way and the
precious diamonds in large number fell helter skelter. Just while this
happened King Duryodhana entered the chamber. Karma was stunned.
Duryodhana said smiling "Shall I help picking up the diamonds?".
Should Karna desert such a friend? No, he would happily die in the
service of such a great King.
Karna's narration of the incident is there in two vembas and an
intervening prose passage. The explanatory prose passage name the
Queen as Lekshasai".
Pampa's Vikramarjuna Vijaya(page 103) gives a similar encounter (which isn't described by the author) but gives a few details that further answer your question.
6E III. BHANUMATI PLAYS A GAME OF DICE WITH KARNA
Another beautiful variation common in Perundevanar and Pampa is the
description of a game of dice between Karna and Duryodhana's queen
which has already been referred to in detail in the previous chapter.
The only difference in making use of this incident is that Karna
narrates the incident to Krishna in Pampa, whereas it is narrated by
Karna to Kunti in Perundevanar.
Duryodhana’s queen is a character that is almost neglected by Bhagavan
Vyasa. He does not even mention the name of the queen of Duryodhana
anywhere. Even when something has to be said about Duryodhana's wife,
Bhagavan generally uses expressions like Lakshmana's mother,
Dhritarashtra's daughter-in-law or Rajaraja" wife and invariably
avoids mentioning her name. Especially the name of "Bhanumathi” as the
spouse of Duryodhana does not appear in Bhagavan Vyasa's text.
Perhaps Bhattanarayana is the first writer to introduce the character
of Bhanunati and to glorify it in his drama Venisamhara. But even in
Venisamhara we do not come across any description of the intimacy
between Bhanumati and Karna. If it is not entirely a creation of
Perundevanar it might have originated from ancient legend or folklore
Anyway Perundevanar is the first poet to give it an honourable place
in the Bharata poem. The second poet to incorporate it in the Bharata
poem is Pampa. If there is no common source for both of thern Pampa
must have copied it from Perundavanar. The same episode is found in
Villi Bharatham. The description of the incident by Perundevanar Pampa
and Villi is similar in many respect.