June Thornton, a patient at the LGI in the 1970s, told BBC Look North she had witnessed Savile come into her ward and abuse a female patient who was incapacitated.
The petition against the proposals, containing signatures from specialists across Yorkshire and the Humber, was handed to members of the Independent Reconfiguration Panel while on a fact-finding visit to the LGI.
Lead signatory Mark Darowski, a children's intensive care specialist at the LGI, said if paediatric heart surgery in Leeds did end it would mean a three-fold rise in journey times for children needing urgent treatment.