Estevez, 19, who came out to his track teammates earlier in the year, spoke to Escobar about what it was like growing up as a gay athlete and the challenges he has faced.
"I think it was a very successful meeting. I actually got to sit down and connect with him," Estevez said. "Being gay does mean something to me, because it is basically who I am and you are using [the slur] in a derogatory way."
Estevez, who, like Escobar, speaks Spanish and lives roughly three miles away from him in Miami, believes progress was made during their conversation because of the similarities they do share with one another. Burke was happy with the way things went as well and thinks that Escobar, after receiving public backlash, has learned his lesson and is remorseful.
"Words like the ones Yunel used can really affect athletes both in the locker room and at home," Burke said about the discussion. "I think it put a face on the issue for Yunel. I think it humanized the issue of gay athletes for Yunel, and I think Jose did a great job today."
Burke, whose brother, Brendan, died in a car crash in 2010 and was an openly gay hockey player, has been speaking with the Blue Jays' front office and Major League Baseball about ways they can bring more awareness to the subject of equality for gays and lesbians.
In the offseason, Burke, Escobar and the Blue Jays' organization will discuss firmer plans, but there are already ones that have been spoken about -- both small- and large-scale. Blue Jays general manager Alex Anthopoulos told Burke to contact him when he decides what the best course of action will be to reach the gay community.
"The Jays have been great," Burke said. "I think the Jays were embarrassed by what happened. They don't want to be represented that way in the community. That's not the way they want the city of Toronto to see them, and they are making long-term commitments in talking with us about finding long-term productive ways to be involved."
Burke said he is hoping the Toronto fans can forgive Escobar, like he has.
"What I do know is that he made a big mistake, and now I think he is sorry for it," Burke said. "Whatever he thought he was doing is what he was not doing. Now we are going to try to come out of it with some positive results.
"After meeting with him, I like Yunel. I think he did a stupid thing, but I think he has learned from it. I hope that, like all of us at You Can Play, I hope the fans of Toronto are willing to give him a second chance. Just a second chance, if there is a third chance, we will be booing him, too."
Estevez spoke about how difficult it was being a gay athlete and that he was often the target of derogatory remarks before he came out. Burke is hoping that culture will change in the future and believes progress is already apparent with the way the Escobar situation was handled.
He believes that even four or five years ago there wouldn't have been such an outcry from the public and admits that it was nice to see how many people condemned Escobar's decision.
"Now the media, the fans, the other players, the front office, everyone is coming together to say, 'We don't want this in baseball, we don't want this in the Toronto Blue Jays, we don't want this in the city of Toronto,'" Burke said. "I think it is very encouraging that there was an outcry about this."
Manager John Farrell said this entire ordeal has been difficult on Escobar, because he believed all along that he was doing nothing wrong. The slur Escobar used is common in the locker room among Latin American players.
"I think he is surprised, because there was never an intent to offend," Farrell said. "That's not to say ignorance is acceptable, but there was never an intent on his part to offend any one person or group.
"I don't think he will be surprised if there is backlash. ... I do know this: In the conversations when he came back after the three-game suspension, he is remorseful. He knows what took place was a mistake -- a mistake that he made and an error in judgment and is fully accepting of the consequences, whether that was at the time or [if] they linger on."
Farrell said he had considered not playing Escobar on Thursday.
"Considered, but I view these situations as there is going to be a first at some point," Farrell said. "So, you know what, he is part of our team, he has been playing for us regularly. To make more of an issue out of this, and that's not to be insensitive in any way. Let him take the field. Go play a game."