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Tansy's dad Damien said he had been waiting for the right time to release the video, for fear of a backlash.
A spokesman for the Aspinall Foundation said the video had been released as part of a fundraising campaign - to highlight the foundation's work in sending captive-born animals back to the wild.
She said: "The video demonstrates clearly the incredible bond of trust which exists between man and one of his closest cousins.
"Helping these animals Back To The Wild is The Aspinall Foundation’s way of repaying this trust."
The Aspinall Foundation needs help with the enormous cost of sending gorillas Back To The Wild. Please donate by visiting www.aspinallfoundation.org/backtothewild
Donations of £3.00 can be made by texting BACK to 70300.
For more on the work of the Aspinall Foundation and how they help endangered western lowland gorillas, click here.