Contrary to a persistent geographic myth, there is no piece of Delaware inside New Jersey. The two states share a border defined by the Delaware River and Delaware Bay, but Delaware's territory does not extend into New Jersey.
The confusion may stem from:
Both states have clearly defined, internationally recognized borders. If you're curious about the actual Delaware-New Jersey boundary, it follows the thalweg (deepest channel) of the Delaware River and the mid-line of Delaware Bay.