From Naval Historical Facts:
GEEDUNK - To most sailors the word geedunk means ice cream, candy, potato
chips and other assorted snacks, or even the place where they can be
purchased. No one, however, knows for certain where the term originated, but
there are several plausible theories:

1.) In the 1920's a comic strip character named Harold Teen and his friends
spent a great amount of time at Pop's candy store. The store's owner called
it The Geedunk for reasons never explained.

2.) The Chinese word meaning a place of idleness sounds something like gee
dung.

3.) Geedunk is the sound made by a vending machine when it dispenses a soft
drink in a cup.

4.) It may be derived from the German word tunk meaning to dip or sop either
in gravy or coffee. Dunking was a common practice in days when bread, not
always obtained fresh, needed a bit of tunking to soften it. The ge is a
German unaccented prefix denoting repetition. In time it may have changed
from getunk to geedunk. Whatever theory we use to explain geedunk's origin,
it doesn't alter the fact that Navy people are glad it all got started.