transmission recalls on 2003 odyssey
None that I'm aware of but check your VIN with a Honda dealer, they can tell if any open recalls exist.
As stated before, Honda will answer your question. On a side note, they have known issues with auto trans used with their v6's. If it breaks and you complain enough, and mention Honda Customer Service, they will fix it free.
There was a recall back then to install an oil jet shooting at the second gear to reduce overheating. However, if overheating has occurred already, loss of reverse is possible. Honda is willing to replace the whole tranny when this happens. They call it goodwill.
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