It is believed the signatures of Lennon's sons Sean and Julian are among the graffiti scrawled on the perimeter walls.
Police said the dealer made contact after wide-spread publicity surrounding the disappearance of the wrought-iron gates from Strawberry Field on Friday.
Children reported men cutting down the 8ft high gates and driving them away in a Transit van.
The Salvation Army home, a childhood haunt of John Lennon, was immortalised in a 1967 Beatles song and has become a shrine for visiting fans.
It is believed the signatures of Lennon's sons Sean and Julian are among the graffiti scrawled on the perimeter walls.
The late singer-songwriter spent much of his youth playing in Strawberry Field's grounds, close to the Menlove Avenue home of his Aunt Mimi with whom he lived as a child.
The line "nothing to get hung about" was inspired by her warning not to play in the grounds, which in the 1940s and 1950s were sprawling and overgrown.
According to Beatles buffs, the young John would reply: "They can't hang you for it."
'Great news'
At first, it was feared that the 100-year-old gates might have been stolen to order for a Beatles fan.
After they were recovered, Beatles expert Phil Cappell said: "This is great news for Beatles' fans. It is what we had been hoping for. They are part of the heritage.
"I think serious consideration must now be given to the security of them.
"Our real worry was if they had been melted down or someone just thought they were too hot to handle and just threw them in the river. They would have been lost forever."