The prince even tried on her Team USA jacket, leading many to speculate about a budding romance for the world's most eligible bachelor.
But Harry will have to keep his Brit mitts to himself, as the 25-year-old is married to bodybuilder Colton Wasil.
Marks, an Army combat medic, suffered a serious hip injury while serving in Iraq in 2010. She took up swimming during her rehabilitation and has won four Invictus medals.
But the swimming champ is lucky to be alive after suffering from respiratory distress at the 2014 Invictus Games in London, when she was put on life support.
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Doctors at Papworth Hospital in England saved her life before she was transported to an Army hospital in Germany.
"But they absolutely saved my life and I can't thank the U.K. enough for having that kind of medical support and taking such good care of me," she told the Press Association.
Remembering those life-saving efforts, Marks gave a gold medal back to Prince Harry as he presented it on Wednesday, instructing him to give it to Papworth Hospital as a sign of her gratitude.
"I gave Prince Harry one of my medals and hope it will find its way back to Papworth," she told the Press Association.