Off-the-field problems and mistakes not related to football are what people remember -- and there have been plenty this season.
It started with Burress' decision to skip a team meeting in September for a so-called family emergency -- and not inform the team. Then, he verbally abused an official two weeks ago before missing a treatment before the Pittsburgh game and being benched for a quarter.
It has cost him money, time and the patience of several teammates.
Despite it all, Burress insisted on Wednesday that he is not a distraction, even as the Giants (6-1) prepare for the biggest game of the season, a showdown with the defending NFC East champion Dallas Cowboys (5-3).
"Like I said, I am human," Burress said after practice. "I have made some mistakes. I haven't made the best of decisions, I am aware of that, and I am the first one to look myself in the mirror, be honest with myself and say that. But as far as me going out and playing hard, I am going to keep going out and competing. Like I said, I just keep going out and doing what is asked of me on the football field, and in whatever that role may be I hope I go out and fulfill it."
Fellow receiver Amani Toomer said it has been hard dealing with Burress this year.
He was suspended for a game against the Seattle Seahawks and fined $117,500 for missing the September meeting. He was fined $45,000 by the league for abusing an official after being called for offensive pass interference against the San Francisco 49ers two weeks ago and then he had to watch the first quarter of the Giants' 21-14 win over the Steelers on Sunday.
"He's his own man," Toomer said. "He makes his own decisions and I have to respect that. He knows his decisions affect the team. It's hard to go up to a grown man [and talk] about doing his business the way everybody else wants him to."
When pressed about what might happen if Burress continues his errant ways, the Giants captain wondered.
"I'll be interested to see because I think that it's still a distraction," Toomer said. "It affects our team."
After getting off to a great start, Burress is no longer the No. 1 option in the offense. He had 10 catches for 133 yards in the season opener against Washington and followed that with five more catches for 81 yards and a touchdown against the St. Louis Rams.
In his last four games, he has had 13 catches for 142 yards and two touchdowns.
"I am not getting frustrated," Burress said. "You have to kind of sit there and expect it, so to speak. You can't just expect teams to come out and let you just run up and down the football field. It has been a slow year for a few of us guys at the receiver position. If you look at it and say if we take those 40, 50, 60 yard plays out of the game, those are big plays that change football games, and if you take them out of the game, you have to work around it."
Burress said he has seen more double coverages this season than ever before.
However, doubling up on Burress has opened things up for other receivers.
Second-year pro Steve Smith leads the Giants with 29 catches for 299 yards, with Toomer third with 22 catches for 277 yards and a touchdown. Domenik Hixon, who started when Burress was suspended, has 13 catches for 220 yards and a touchdown and tight end Kevin Boss is slowly catching on with 10 catches for 118 yards and two touchdowns.
Burress opened last season against Dallas with eight catches for 144 yards and a career-best three touchdowns. He added six more catches and another TD in the second meeting but was limited to one catch for 5 yards in the playoff game against the Cowboys.
Ironically, the Giants won the playoff game and lost the other two.
Cowboys coach Wade Phillips said he does not plan to let Burress run free on Sunday.
"You have to double him, you have to double him," Phillips said. "He is just a good receiver. [Eli] Manning can get him the ball in all kinds of situations. You just have to double him as much as you can. We tried to do that. We will try to do that this game."
Burress welcomes the attention.
"If the team is going to line up and take me out of the game, then those are things that I have no control over," Burress said. "I control what I control and when the opportunities are presented to me to go out and make plays, then I do and because of that we are a 6-1 football team."