While I am not certain that you have the correct diagnosis.....fresh water dips must be of similar temperature AND pH to the saltwater tank the animal comes from to make it as stress free as possible. Most people will leave the animal in for 3-5 minutes. Best to move the water withion the container with a small power head or plastic spatula. pull him out if he appears stressed...swimming more erratically....
I have not kept an eel. However, with fish many times Methylene Blue can be added to the dip water as it is reported to reduce stress/soothe the gills.