Yeah, that's a manager fail. Telling the guy who works in the back of house and does harder labor to be mindful of how stinky he's getting for the 1% of the time he might get called up to the register? That's ineffective advice that makes him worse at the job he does 99% of the time. And putting the complaint up front is hugely demotivating to the employee, and it rewards the customer for complaining, leading to more nitpicky complaints.
The customer is getting worked up over an imaginary problem, too. Smelling some B.O. at the register doesn't harm anyone. At worst it's a little unpleasant, and life is full of little unpleasantries. I'll argue that their problem is largely symbolic, not realistic. They're upset about the idea of B.O. near their food more than the actual smell. Their food isn't tainted, and they will stop smelling B.O. seconds after they leave the register.
Body Odor has not always been treated as offensive. It depends on a lot of cultural and historical factors. No one in their right mind would complain about a mailman in 1870 smelling like B.O. and Horse, or a hot asphalt worker smelling like hot tar and armpit. The idea that it's offensive to come to work with noticeable smell is a more recent invention of the post-industrial age. It's the switch from a predominantly agricultural society to a predominantly desk-worker society. Email jockeys, dentists, or customer service workers who stand around all day don't have the expectation of getting sweaty.
We also get chemical companies inventing products that cover up odors (Listerine! Deodorant! Febreeze!) and they market those odors as an urgent problem to make us buy them. But if we step back and look at different historical eras next to each other, we see that the smells problem is not so urgent. For one, there are worse smells than B.O. or bad breath we deal with every day. Car Exhaust! Manure fertilizer! Your cat's litter box! Deep fryer oil! The thing is, the way we categorize and rank those smells is more about social constructs of acceptability than it is about how bad they actually smell.
Which brings us back to our fictional upset customer. They're concerned that the food might get 'tainted' by the smell of body odor. This is wild, and it shows they've never worked in a commercial kitchen. Food processing is bathed in bad smells, from farm to table. Those veggies were grown in the dirt, washed in toxic chemicals, carried by workers in the hot sun, before eventually getting washed and wrapped in sanitary-coded plastics for sale. The livestock whose meat and eggs and milk you buy are raised in farms, covered in sweat and their own shit and urine before they get processed into the clean-looking products at the grocer. The food you eat at a restaurant is made in a hot kitchen by a bunch of underpaid, chain-smoking, sweat-covered, and bloody chefs. They all stink like sweat and grease before your omurice gets to the table.
What the customer is really upset about is the symbolic contamination of their food, which exposes the literal contaminations that are an inherent part of the food industry. All that food on display is wrapped in plastic to maintain the symbols of purity and sanitation. Bringing the back of the house up front exposes the mythology for what it is- a story about cleanliness. A story told with signs and rituals that launders all the filth and environmental destruction and social murder that our modern society is built on.