Jones became head coach of his native Australia in 2001 and guided them to the World Cup final in 2003.
During this summer's series down under, Jones said the Australian media had an orchestrated campaign against his side.
"There was a lot of vitriol about Australia, his home nation," said Cheika of Jones during the summer tour.
Cheika, a former team-mate of Jones at Sydney side Randwick, added: "It's where he coached, where the opportunities were given to him to grow up as a coach, and play.
"Personally if you're looking to leave a legacy somewhere, you don't want to hit back at it when you leave."
Under Jones' guidance, England completed a series whitewash in Australia in June, becoming the first touring side to secure a 3-0 series win down under since South Africa in 1971.
And they will aim to create more history when they host the Wallabies at Twickenham as victory on Saturday would equal England's record of 14 consecutive wins, set under Sir Clive Woodward in 2003.
Jones, however, has once again raised tensions ahead of Saturday's match by asking for a meeting with referee Jaco Peyper to address the Wallabies' scrummaging technique.
Cheika said: "I suppose it's always difficult when you go back into a tournament where you're playing teams you've coached before.
"And you don't really know how to play it, do you stay reserved or do you go out there and get stuck into them? I know what I do, even in a country like Ireland when I'm there where I coached for many years.
"I didn't coach the national team there, but that's the choice he wants to make, and he thinks is best for his team."
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England boss Eddie Jones has tarnished his legacy in Australia because of comments made during the summer, says Wallabies head coach Michael Cheika.