She brought up the license of trade and all that when she was grilling him about how fraudulent his business was, but she never used the health code violations clearly committed by Nick and his buddy even though she witnessed their entire unsanitary popsicle-making operation, in her argument-- a point which I'm sure Nick wouldn't easily pull up a license for to shut down.
Earlier in the movie, before she realised she'd been scammed, she told off the elephants about their ungloved trunks and how that was a serious health code violation. This proves that she is well versed in zootopian law, specifically health and safety regulations.
She saw Nick melt the popsicle down somebody's unsterile roof and down an old pipe (probably rusty and riddled with God-knows-what type of microbes and grime), then poured into paw prints (made by paws that walked all over the city, stepping in who knows what all day) in the snow to freeze back into miniature paw-shaped popsicles! POPSICLES which were then sold and EATEN by hamsters and other mammals! Those hamsters might as well lick the city's sidewalks because doing that and eating those popsicles is basically the same frigging thing, germ-wise.
Like, she noticed all the necessary lacking licenses and all that but she didn't notice THIS? She could have used his business to put him out of business, lol. She could have waited for the next day, tailed him covertly, then filmed him go about his business of making popsicles which probably smell like feet (and which Nick later eats himself rolls eyes) and used that as evidence against him.
And that's it, her win the b-a-g; smart bunny, dumb fox.
Maybe she didn't think of it when in mid-argument with Nick, but like, COME ON JUDY!