I am not sure the year that Honda stopped calling their van towable behind RV's, perhaps 2004 or 2005? However Honda did not make any real changes to the transmission in that year, they just stopped recommending it as towable.
It might have something to do with how well the hitch is attached to the front of the car, more than any warranty failures that Honda might have had to pay for in those years (such as a possible transmission damage warranty problem).
I would want to inspect the area that the hitch attaches to the frame, make sure that the frame is not cracking away from the rest of the car. Honda makes the front area in front of the passenger compartment a "Crush Zone" for the 30 MPH crash into the wall test, and does not design the car to be towed. Other companies make the hitch brackets, and attach to this frontal sheet metal. My Honda CRV had a set of long rods that attached about 3' behind the bumper to a bolt that Honda put there (the kit came with a 10 mm longer bolt to replace the Honda factory installed bolt). I think this helps to strengthen the attachment of the towing brackets to the chassis.
In the Honda's owners manual for my CRV, they state to warm up the car engine for 5 minutes before towing. This thins out and warms up the transmission fluid, as well as recharge the battery a bit. Then shift to Drive, then shift to Neutral, then turn off the key, but do not put it in the "Lock" position, as that will cause the steering wheel to lock. It will be in the "ACC" position, so turn off the radio, and you will need an additional key to lock the doors and get back into the vehicle after you arrive at your destination.
Also I was talking with a couple of Honda engineers, and suggested that the engine be started and run for 5 minutes every 300 miles. This lubes the transmission again, recharges the battery a little more, and you are ready to tow some more. So at each fuel stop, I would start the car, let it run until ready to go again. And if I spent a hour at a rest stop, I would start the car a few minutes before leaving, then shut it off again. Leave it in neutral, and it is OK.
I have towed a 2003 Honda Pilot--same transmission--over 80,000 miles. First behind a 30 foot gasser V10. Now a 8.3L diesel. Weight is not a problem with these vehicles for most RV's. Many gassers are rated to tow 5,000 lbs, our pusher is rated for 10,000 lbs.
The 2003 Odyssey weight is about 4,400 lbs.
You want a brake supplement. We use a bake buddy.
The lights have to be hooked up. We had this done professionally.
Run the engine thru the gears--but never go reverse to neutral for tow--go low gears to drive to neutral. 5 minutes at start and every 300 miles is fine. We did put in a charging circuit because of battery drain by brake buddy.
Tow in neutral, key in first off position--turn all radios etc off. Check to be sure that the wheel is free to turn. Check in re view mirror on your first turn. Be sure that tow bar is level (we have a 4" step up adaptor to our hitch.
Bob and Marie Austin
Angel miniature poodle
2007 Holiday Rambler Ambassador 40 PDQ
Toad 2012 GM Yukon XL 4 x 4