The meeting, a week ago Thursday, focused on what Hardy can do personally to avoid creating negative issues for himself, according to the sources.
Jones declined to speak specifically about the meeting after the Cowboys' 24-14 win over the Miami Dolphins, but he did say Hardy is trying to change his behavior.
"He is aware that everything he does -- his personality, his style, his enthusiasm -- it's all going to be interpreted negatively," Jones said. "If he's not aware of that, then he's hurting a lot of people.
"I think he really gets that. We certainly feel that way. He understands it, and he has agreed to really work on it."
Jones said he's used his own experiences with criticism from the media to explain to Hardy why modifying his behavior will ease the scrutiny he receives.
"If anyone knows how to hunker down, it's me," Jones said. "I know when you've lost all your benefits of the doubt and you so much as run as a stop sign or step out of bounds you're fixing to answer a lot of questions."
The NFL suspended Hardy for the season's first four games for violating the NFL's personal conduct policy during an alleged domestic violence incident. Two weeks ago, the website Deadspinreleased photos of Hardy's alleged victim, which shows her with bruises on various parts of her body.
Since the photos were released, Hardy has been either late or missed several meetings. The day Jones met with Hardy, the defensive end missed that morning's meeting and practice.
Jones said Hardy's behavior on and off the field was good during training camp. Since he returned from his suspension, Hardy has created issues for himself with controversial comments about Tom Brady's wife and some Tweets that showed poor judgment.
He changed his Twitter bio to indicate that he was innocent of the domestic violence allegations but later changed his bio again after speaking with coach Jason Garrett.
"I don't think it has been easy for him," Garrett said earlier this week. "I think he's doing his best to handle it every day. He a highly scrutinized guy, and what we're trying to do is create an environment for him where he can be his best."
It hasn't helped Hardy, said Jones, that the Cowboys had lost seven consecutive games before beating Miami on Sunday. Losing so many football games, he said, breeds a negative atmosphere.
Hardy has been strongly criticized nationally and locally. Jones said the criticism has affected Hardy.
"I will say this: Over the last three or four weeks, I would hate to see anybody who had more pressure on him than Hardy," Jones said. "There is a genuine effort for him to rehab what is the perception of him.
"But there is no second chance in regards to the issue of domestic violence. None."
Looking ahead, he was asked Sunday if the Cowboys' next game against the Carolina Panthers, Hardy's former team, means anything extra to him.
"Just a nameless, faceless opponent," Hardy said. "Next game. Got to stay focused."
How does he keep the Panthers as a nameless, faceless opponent?
"Just stay in the game with my teammates," Hardy said. "Got a great bunch of guys. And focus on the next game."
Information from ESPN's Todd Archer was used in this report.
Hardy on Panthers: 'Nameless, faceless opponents'
Cowboys DE Greg Hardy refers to the Panthers, his former team, as "nameless, faceless opponents" and explains that he's already focused on the next game and is no longer thinking about Dallas' win over Miami.