"I texted her saying "is this the right one", and she said, "no you want parchment paper", and "I'm like where's the parchment paper?!"
"It was nice, I had a baseball cap on, looking down at the floor, trying to stay incognito. It's amazing how much chewing gum you see, it's a mess!"
There must have been some kind of magic brewing as we all know the couple went on to tie the knot at St George's Chapel in Windsor on 19 May 2018.
They welcomed their first child, Archie Harrison Mountbatten-Windsor, on May 6 2019 and are now expecting their second child together.
During his wide-ranging chat with Shepard, Harry was also asked about what it was really like to be married to a prince.
The soon to be father-of-two said his wife had had the "most amazing explanation for this."
Prince Harry also opened up about his decision to leave the Royal Family because he realised in his 20s his life was "a mix between The Truman Show and living in a zoo."
"It's the job right? Grin and bear it. Get on with it. I was in my early 20s and I was thinking I don't want this job, I don't want to be here. I don't want to be doing this," he said.
"Look what it did to my mum. How am I ever going to settle down and have a wife and family, when I know it's going to happen again?"
The royal says he turned to therapy to navigate his mental health after Meghan "saw he was angry."
"Once I started doing therapy it was like the bubble was burst. I plucked my head out of the sand and gave it a good shake off and I was like, 'You're in this position of privilege, stop complaining and stop thinking you want something different - make this different - because you can't get out," he said.
"'How are you going to do these things differently, how are you going to make your mum proud and use this platform to really affect change?'"
This story originally appeared on our sister site Now To Love