Facing them earlier this year, he ran for 113 yards and two scores in a blowout win.
On Sunday, he faces the Washington Redskins, another team that cut him.
"I hope I have the same reaction when I go against them," Brown said with a laugh Friday.
After missing last week's game with a concussion, Brown was cleared to return to practice this week and is probable for Sunday's game against the Redskins. The running back could potentially be right back in the mix, as starter Ahmad Bradshaw is questionable with a foot injury that forced him to miss two days of practice this week.
"Everybody has a role on this team," Brown said. "You just have to make sure when your role is called you step up and perform, so I look at it every week just go in there, be humble, work hard and be confident enough to perform if my number's called."
Brown ran with his chance earlier this year, when Bradshaw hurt his neck against the Tampa Bay Buccaneers in the second game of the season. He stepped in with 90 total yards and a touchdown to help the Giants comeback and defeat the Bucs, and the following week he started against the Panthers and played the best game of his career.
Bradshaw returned the next week against the Philadelphia Eagles and Brown had only five carries, and then he suffered a concussion on a kickoff return the following week against the Cleveland Browns. After being cleared, he said he feels great and is ready to go out and help the team whatever way is needed.
"Nobody wants to get hurt, that's the worst thing about it. If you can play football and not be hurt that'd be awesome," Brown said. "The fact that I was having such a good little run, it's even more fun to go out there and get to running again. Just go and play all-out and have fun and do what I'm supposed to do."
The Giants' distribution of handoffs on Sunday will be a hotly debated topic, as Bradshaw is dinged up, Brown is coming off a concussion, and rookie David Wilson has had some big plays over the last two weeks. While Giants coach Tom Coughlin said he expects Bradshaw to take on a full load Sunday, it would not be surprising if the Giants reduce his work in light of the injury.
Brown said he's been told to make sure he knows his pass protections this week, and there have been no different instructions than usual from the coaches. He's looking forward to getting his chance to return to the field Sunday, especially against one of the five teams that have cut him during his career.
"It wasn't bitter. It was business," Brown said. "It is what it is. I just go out there and have fun and play ball."