The US President, who arrived in London to attend the G20 summit, had presented the royal with a personalised iPod during the historic meeting at Buckingham Palace.
The 82-year-old Queen, an iPod fan, who already holds a 6GB silver model, was presented the gadget containing photos and a video of her last visit to America in 2007.
The American leader's thoughtfulness was further unveiled when he gave the royals a rare signed songbook by Richard Rodgers - one of Her Majesty's favourite composer.
The Queen, in return, gave the First couple what she always gives a visiting dignitary, that is, a signed photo of herself and Prince Philip in a silver frame.
Obama had last faced controversy over gift-giving when he presented British Prime Minister Gordon Brown a set of DVDs during his visit to the White House.
And this time also, his choice of present has not escaped the criticism of renowned etiquette expert Anna Post of the Emily Post Institute.
"For me, the iPod only works if he has some catchy reason why he gave it as a gift," the Politico quoted her as saying.
"Otherwise it feels like somebody at the White House pulled the lever and an iPod is what popped up."
"And if it was just pulled out of the blue, you run the risk of the 'Oh, how nice,' reaction from people which is the polite gloss of, 'What on earth am I going to do with this?'" she added.