On Independence Day, Rylan was delighted to share some advice from viewers with the grandma-to-be during lighter moments of the former First Lady's appearance.
"You should refuse to change the nappy from day one or it's gonna become your responsibility, Hil - and you don't need it, you don't need it, babe," the presenter enthused.
Back in the main studio, Eamonn Holmes had his head in his hands.
"Did you just call the former First Lady, the former US Secretary 'babe'?" he groaned, to laughter from the woman in question. "Back in the cupboard!"
He's adorable - take him out of the cupboard!
On a more serious note, Eamonn did his best to get Mrs Clinton to confirm whether or not she would again run for the presidency.
"You so know. You so know you are. You might as well tell me," he persisted.
"I don't know!" she laughed, finally seeming to convince him.
Mrs Clinton was a Democratic presidential candidate in 2008, losing out to Barack Obama before ending up as his Secretary of State when he went on to become the 44th president.
Promoting her book, entitled Hard Choices, she spoke about how difficult it was to accept that position in the Obama administration under those circumstances.
"Did he come into the room, like Rylan, all 'Hils, babe ...'" Eamonn suggested.
"We met, it was like an awkward first date between teenagers ..." Mrs Clinton said, of that first meeting with her rival after the primaries.
"We sat and talked and cleared the air ... What I told him was exactly how I felt. It had been hard-fought - he won, I lost, and I was going to do everything I could to get him elected as president."
You have to make these decisions and you know you're an imperfect person and you know you have imperfect information - and you know that, no matter what you decide, there will be consequences.
With her book focusing on the hard choices reflected in the title, Mrs Clinton touched on both political and personal decisions that she had been called on to make over the years.
And of course that included standing by her husband Bill, despite his well-documented affair.
"For me it was a very hard choice, but the right choice, to choose forgiveness and to continue what had become just a central part of both of our lives ..." she said.
"I'm very grateful that that's the decision that I made, but I'm also very respectful when others make a different decision."
While Mrs Clinton believes she would have made the same decision if she was not in the public eye, she notes that it is hard to "listen to your own heart" and not be swayed by outside opinions.
She also jokingly added of her husband: "I knew he was trouble from the moment I met him. That's why I turned him down twice when he asked me to marry him!"
As for Mr Clinton's thoughts on his wife possibly undertaking another gruelling presidential campaign, one which is sure to throw their personal life firmly back in the spotlight ...
"He says very clearly he will support whatever I decide, and that's the right attitude. That's always what I've told him," Mrs Clinton said.
In one last-ditch effort to get a hint on her decision, Eamonn asked coyly: "So if Ruth and I come and visit you in, say, three years' time ... Will we need security clearance?"
To which the reply was: "Well, Ruth will always get through!"