Short answer
First, try to estimate how much eel was eaten and whether it was plain or seasoned. A small piece of plain, cooked eel is often okay, but eel is very high in fat which can cause pancreatitis. Watch your dog closely over the next 24 hours for signs like vomiting, diarrhoea, or a hunched, painful abdomen. If your dog ate a large amount, or if you see any of these warning signs, it's time to call your vet.
Eel — Food safety facts
Feed with care · Dogs · full breakdown on the linked food page
Very high in fat, and raw eel blood is toxic. Cooked plain in tiny amounts only.
The full verdict, portion guidance and serving notes are collected on the Eel food facts page.