If you order the official Jazz detachable towbar from Honda, your local dealer will fit it, and no it does not cut any bodywork.
Yes it is made by Bosal.
It is both excellent and useless. I shall explain. The idea is brilliant, when fitted in place its a good height. Brilliant for small camping sized trailers, but it struggles pulling an overall weight of more than half a ton even with the 1339 engine. If you have rear parking sensors you'll find they go bleeeeeeeep when in reverse because your Jazz will think its reversing into the trailer you are towing LOL. Also I think the ball itself is a tiny bit small - my little trailer creaks behind my Jazz but not when being towed by our other cars.
However the mechanism is an absolute pig. You need the strength of a wrestler to turn the big button to get it into the green locking position to attach to the car. I've snapped one of the keys provided. Now mine, with precious little use and perfectly stored, has broken so is impossible to attach onto the car. I've tried soaking the device in penetrating fluid but its not playing ball. I think the replacement detachable part is the same used on the CRV, and will cost £150+ to buy direct form Bosal. Very frustrating.
Oh and the plastic clip provided when the towbar isn't in place does not fit well. And the metal frame rusts.
So in hindsight, not a lot of towbar for the £500 or whatever it costs now from Honda.
If I had to buy one new, I'd consider a fixed type, or maybe a Witter if they do one for the Jazz GE becuase their detachable mechanisms seem far easier and better.