When surgeons invert a penis they can't get rid of the epidermis or stop it from acting like epidermis. to tl;dr this, your skin is your first layer of defense against pathogens and parasites. This is why the outer later is dead cells, but they are coated in oil. The oil both hydrates the dead epidermis to keep it from drying out and at microlevels, oil is like trying to move through tar. Even if they make it through the car, all they will find is dead cells that are not very digestible. And your body keeps making more cells and more oil, a mixture called sebum.
This stuff is supposed to rub/wash/flake off naturally, just fall away. When it cannot because of man-made surgical horrors, it just builds up and the oils go rancid. One of the more common places this happens in modern humans is toejam, the build up of sebum under particulary the large toenail. The smell is not fully comparable however because toejam is evenutally removed naturally by your skin growing outwards from under the nail like a conveyor belt. The surgical horror the neogina is not made like that. Unless there deliberate efforts to clean it, it will accumulate.
The other smell will be that of ass. Modern surgical mutilations usually involve taking part of the colon and integrating this with the inverted penis and scrote. They use a part of the sigmoid colon, which... so in digestion the colon extracts water from your poop. This can make your poop too dry, so the sigmoid colon produces mucus to lubricate your kids before you drop them off at the pool so they don't chaff your butthole. Addinf this tissue allows the horrorwound to self-lubriate to a degree. As there is no food processing being done, there would be no fecal odors but it would still smell of the specific brand of mucus your body uses to lube up your logs for final exit.
Oh, there would also be another smell for the trannies having chasers fuck them. Old, mouldering cum. Like imagine the smell of regularly used but never cleaned fleshlight.