As Ms Trench and 007 played cards at the Le Cercle Club casino, Bond says: 'I admire your courage, Miss, er...?', to which Sylvia says: 'Trench, Sylvia Trench.
The news was posted on Gayson's Twitter account Saturday morning.
Speaking about the scene in 2012, Gayson recalled how she helped calm Connery's nerves by taking him for a drink so he could deliver the line correctly. "An incredible lady who left a lasting impression on everyone she met".
Gayson had originally been cast as Miss Moneypenny before the producers chose to replace her with Lois Maxwell and recast Gayson as a femme fatale character.
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Another message from the daughter and stepson of the original Bond producer Albert Broccoli appeared alongside a picture of Gayson in character as Trench.
She was remembered by James Bond franchise producers Michael Wilson and Barbara Broccoli, who paid tribute to her from the official James Bond Twitter account.
Originally, Gayson was meant to play M's secretary, Miss Moneypenny, but Lois Maxwell landed that role instead.
Sylvia Trench was due to be a recurring character, but the idea was dropped by the director of Goldfinger, Guy Hamilton.
Gayson's voice was dubbed in both films by German voice actress Nikki Van Der Zyl.
The Surrey-Born beauty also played the part of The Baroness in the London stage production of The Sound Of Music before going on to land other film roles.