When someone brings up an old grievance that was dead and buried and attempts to revive it to suit their purpose. For example, say a woman named Katie dislikes the fact that one of her friends has bought something Katie wanted for herself. Instead of simply stating annoyance just about that, she also starts referencing a time when they were in school twenty years ago and her friend had kissed a boy that Katie had liked herself. That's a dusty grudge.
Similarly, when someone gets personally annoyed about something which happened many years before they were even born and starts flapping gums about it and getting all irate; that too is a dusty grudge. For example, a black friend on a night out does not take too kindly to the request from his white friends that he to go to the bar. Rather than tell them to go themselves, he then journeys a bit too far off the freaking scale and starts huffing and puffing about slavery and opression of black people in the 1700's. Extremely dusty gruge.
woman- "No, Trina and Tash are fighting, so we can't invite them to the party."
man-"Still? What is the problem now?!"
woman-"Well, first it was because Trina asked Joey's dad out to the single parent's coffee morning and Tash had been saying she like him, but now it's about Trina deliberately wearing the same colour dress but much shorter than Tash's to her brother's bbq in 1995."
man-"Fuck me, that's a dusty grudge if ever I heard one!!"
Fred- "Are you getting your ticket now, Blake?"
Blake "Yeah, why?"
Fred- "Could you grab mine too, please? Here's the money, I just want to use the toilets first."
Dave- "Yeah, me too, if that's ok, Blake?"
Blake- "You know what? Fuck this!! I didn't come out to be the token fucking slave!! Yeah, SLAVE. I said it. People like you are why the slave trade kept going for so damn long!! I don't have to do things for you just because I'm black!! What is it like ingrained in you white folk that we're you're servants?! Well, no more!!! NO more."
Dave- "Jesus, Blake. Were you a part of the fucking slave trade?! Massive overreaction there, mate!"
Fred-"Yeah, I second that. All you had to say was "No." That's a seriously dusty grudge you've got there."