Speaking on his BBC Radio 1 show, Greg said: "They were listening on the morning Charlotte went to school.
"I saw the photo during the show and said, 'Who the hell shakes hands with their teacher on the first day?'"
Greg said in the weeks following, he was invited to Kensington Palace along with Radio 1's Teen Heroes.
Greg continued: "They said, 'We were listening on the morning of little Charlotte's first day, and we want to talk to you about the handshaking thing...
"I went: 'Oh God, no!' They'd heard me saying this school was so posh they had to shake hands with their teacher every day.
"They were not like that in my day. You were pleased if you got a smile."
Luckily for Greg, Kate and William saw the funny side and he added: "I'm sure it's all absolutely fine."
Thomas’s Battersea describes itself as a Christian school.
They are open to children of all faiths and believes in “praise as the greatest motivator”.
Parents are told their children will be in an atmosphere which seeks positive relationships between pupils, teachers and parents.
George, who is six, started at the school in September 2017.
Art, ballet, drama, ICT, French, music and physical education are all taught by specialist teachers from a child’s first day.
The school is housed in a Grade II listed building, the former Sir Walter St John’s Grammar School which dates back to 1700.
In the past, William said his son “absolutely loves ballet”.