Madine, on loan from Cardiff City, will miss his team's forthcoming games against Bristol City and Preston North End as he completes the three match ban he was handed after being dismissed against Brentford earlier this month.
Given his colourful and often controversial past off the pitch, something he acknowledged after being unveiled by United earlier this year, Madine's dismissal inevitably prompted suggestions he could not be trusted as United attempt to plot a course into the Premier League.
But, reminding the facts reveal a different story, Wilder insisted it would be wrong to portray the 28-year-old as a recalcitrant player.
Pointing to a disciplinary record which has seen Madine sent-off only twice in his 12 season long career, the United manager said: "We all hear the stuff that gets thrown about but, in this case, I don't think it's fair. It's not like Gaz walks three or four times every year is it. In fact, I think that was only his second or third red since turning professional. So that tells you something different doesn't it."
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Although Wilder acknowledged Madine could have few complaints about the referee's decision following his foul on Ezri Konsa - "Gary made a bad call," he said, after United recovered to record a 2-0 win - both he and captain Billy Sharp later admitted they were impressed by the striker's reaction.
"In this day and age, especially with it being so easy to get booked and because he's a whole-hearted lad, I think that record in actually pretty damn good," Wilder continued.
Despite his combative nature, Madine has actually been cautioned only 32 times as a professional; an average of 2.6 per campaign. Neverthetless, it is imperative he learns the lessons of his mistake against Thomas Frank's side given his importance to a United squad which entered the international break second in the Championship with only eight fixtures remaining.
With Billy Sharp, David McGoldrick and Scott Hogan among those at his disposal, Wilder has enough attacking options to devise an effective game plan for the meeting with Lee Johnson's City. But his absence could prove an issue at Preston North End, where Alex Neil's men are likely to adopt a more physical approach than the visitors from the south-west. Preston, who travel to Reading next weekend, are unbeaten on home soil in the league since Boxing Day.
Madine's physical attributes also appear perfectly suited to games against the likes of Millwall and Ipswich Town, who United must also face between now and May."We've got different facets up there now," Wilder said. "Experienced ones too, which hopefully is a good position to be in."