On Friday, the pregnant royal and her husband Prince Harry, stopped at charity One25, which specialises in helping women to break free from sex work and provides practical and emotional support, including expert advice, crisis care, hot showers and lunch.
"Do you have a sharpie?" she asked, according to video of the visit.
According to a Kensington Palace spokesperson, Meghan "learned of this idea from an act of kindness by a school cafeteria worker in the US who wrote messages for children".
The Duchess took inspiration from a canteen manager in the United States, who wrote affirmations on bananas to make school children feel empowered.
Morgan became heated on the Good Morning Britain segment saying: "If you'd been advising Meghan Markle before this, would you have said maybe not the bananas?"
"Giving prostitutes an "empowering" banana after they've spent the night subjecting their bodies to often vile, sexually depraved men, is quite another [thing]", he added. The sweet gesture was not met with appreciation from one sex worker.
Piers seems annoyed at this banana too
"It sounds really cheesy, but little things like that when you are out - especially tonight with the weather - just to get that little thing [means the world]", she said.
"Meghan is focused on calm and positive energy around the birth - she's a big believer in that", a source told the magazine.
"It's literally like here's Meghan Markle, actress, marries handsome prince, lives in a palace - comes along, picks up a bunch of bananas and says "you're strong" - it's so patronising".
Markle was greeting a group of young children when one particularly precocious boy approached the royal couple and began questioning them.
During her and husband Prince Harry's tour of New Zealand and Australia a year ago, during which they revealed they were expecting a baby, Morgan slammed her as being "fake".
Others defended her on the other hand, and the charity's CEO Anna Smith told BAZAAR.com it was a moment she will never forget.