Ok so I followed charlest directions to the tee twice and as the pictures below show no dice. First picture is before I started.
Frankly I can't particularly see any lines in those pics.
But considering how polished that ball is, I'd say what your probably seeing is track wear not oil.
Being polished that would explain why it (the track lines) come back so fast also, polished ball will show wear faster than a dull ball. Especially if your bowling on a dry condition.
Ultimately though if Clean'N Dull or any cleaner doesn't do what you want, don't use it.