Since those who really know have not yet responded and because your question got my interest up, I am giving a non-expert's answer.
Assuming what you caught was the common native American eel, Anguilla rostrata (brown or yellow eel), and assuming that these are not present in large numbers in your pond, the impact should be minimal. Any you find would be unfertilized females and, as you note, they do not reproduce in fresh water. They can grow to large size over a number of years on a carnivorous diet of live crustaceans, small fish, etc., but their growth is not rapid. The only potential problem I could see would be if an angler inexperienced in toothed fishes were to be bitten by one while removing a hook.
On the other hand, exotic species which can reproduce in fresh water have been introduced to American waters from time to time and have the potential to do great damage. You will remember the northern snakehead scare in Maryland a year or two ago. Also, so-called "rice eels," which are air breathing fish which look like eels but are not and which can migrate long distances over land, have been introduced into North Georgia. Unlike the American eel, they have no pectoral fins. They would be almost impossible to eradicate once established.
If you still have the fish and are not absolutely positive it is a native eel, you would do well to have it identified by an expert.
Lou
