Hayden ignited yet another row between the sides when he called spinner Harbhajan Singh an "obnoxious weed" on Australian radio on Tuesday.
Harbhajan replied by saying Hayden was one of the most disliked players in world cricket.
"Who is Matthew Hayden? You only need to speak to international cricketers... to know in what opinion they hold Hayden," Harbhajan said.
Speaking here, Gilchrist said he paid little heed to Harbhajan's words.
"I've not ever cared to think what other teams think of Matthew Hayden," he said. "He's one of the most well-respected people in our team, so that's all that interests me."
The wicketkeeper-batsman also defended Ricky Ponting, dismissing Harbhajan's claims the Australian skipper used abusive language towards him during Sunday's tri-series game in Sydney.
He said Ponting did not say anything inflammatory during the game, after which India officially complained to match referee Jeff Crowe about the provocative behaviour of Ponting, Hayden and Andrew Symonds.
Gilchrist said the controversy swirling around his farewell international season has worn him down.
The Hayden incident is the latest in a series of controversies, and follows a racism row, threats by India to leave, and players fined for aggressive behaviour.
"Everyone is over it a little bit now," Gilchrist said. "I'm just trying to get on with the finals and play some cricket.
"I can't speak on behalf of everyone, particularly on their team, and I haven't spoken to our guys about it, but I'm sure everyone is just keen to let cricket get on.
"There's been a lot on, a lot of issues, I haven't played in too many summers where... there's been any number of issues you could bring to mind."
Australia play Sri Lanka in a dead rubber on Friday in Melbourne, before locking horns with the Indians again in the tri-series finals, starting on Tuesday.
Gilchrist said it was important Australia remained focused on playing good cricket.