You already know Greg's backstory ... the NFL star was accused of domestic violence against a woman back in 2014 and initially convicted. The conviction was overturned in 2015.

He was also arrested for cocaine possession in 2016.

Hardy was essentially blackballed from the NFL ... so he ultimately decided to train in MMA.

We're told he made a real effort to clean up his lifestyle and focus on the sport -- and so far, he's been incredibly successful in his new career ... racking up a 5-0 record in his first 5 fights.

Now, he's set to fight at UFC on ESPN+ on Saturday -- and acknowledges that his past has become an issue since the card also features Rachael Ostovich, a domestic violence victim.

Hardy tells us he's staying focused on his fight and trying not to be a distraction from all of the other fighters on the card ... since he knows how hard everyone worked to get to this level.

Hardy isn't getting into specifics about his legal past -- but says he's got a new lease on life and a new attitude and wants to be a respected professional moving forward.

As for his fight with Allen Crowder ... Hardy says he wants his opponent to know he's a "very dangerous man inside the Octagon and I'm very serious about what I do."