In The Storyteller, by Saki, when the aunt says "You have undermined the effect of years of careful teaching." What does that mean?

In order to answer this question one must understand H.H.
Munro's (Saki's) writing style and purpose.

Saki is a late
Victorian to Edwardian-era writer whose style is very much comparable with the styles of
Oscar Wilde, PG Woodehouse, GB Shaw, and Evelyn Waugh.

This
being said his stories are oftenled by an idle dandy or, like in this particular story,
a bachelor. Saki, in tandem with the writings of Wilde, is also fond of epigrams and
contradictions in his stories. Therefore, his writings will always end in a
twist.

In the short story The
Storyteller, an aunt and her two nieces and nephew travelled by carriage
sharing the same cart with a bored bachelor who was not related to
them.

One can see that the aunt is a very prudish and
annoying woman with no control of the children. She also appears to be into virtuous
behavior as evidenced in the boring tale she told the children about how good people are
rewarded and bad people are not.

When the children express
their dislike about the story, the bachelor makes a smart comment to the aunt to which
she responds angrily by challenging the bachelor to tell the children a story
himself.

Hence, the bachelor tells the kids a tale about a
very good little girl who gets rewarded by the Prince with medals of good conduct, and
by being invited to visit the the royal private gardens. However, the ending of the
story is that a wolf entered the gardens, ate the girl "in a morsel", and the only
things left of hers were her three good behavior medals. This was an ironic tale which
made the kids laugh and deem the girl as "horribly good" and the story as a "beautiful
story".

Therefore, the reason why the aunt tells him that
he has undermined the effects of years of careful teaching means
that, as much as the children have been taught to be good, here comes this guy out of
nowhere to switch the way they saw things: Good girls, such as the girl in the story,
still got eaten by the wolf.

The bachelor simply made the
bad look good in the eyes of the children to the dismay of their prudish
aunt.