Don't Pour it down the sink!First thing is a potato or starch to absorb the extra spice. Take a raw potato, peel it, cut in two or 3 pieces, (if it is a good size). You will be tossing it out later...
I would expect that since it is a spice the addition of fat should mellow the ginger's flavor. You could also dilute the soup with more stock or cream to lessen the taste.
Unfortunatly there is not much that can be done in this case.
Black pepper should be used in small amounts near the end of cooking as a final seasoning.
If its to peppery then you might be better...