The operation that reverses pile shuffling is more pile shuffling.
If you pile-shuffle n card in k piles, and do this i(n,k) times, you get back to the original order. That this is true is trivial, there are at most n! orderings, and as it is deterministic, it must repeat itself eventually*. But i(n,k) is way smaller than n!.
Also, you could revert a pile shuffle by taking the "shuffled" deck, take k cards each, put them into a pile and than draw 1 card from each pile rotating. So just think on what you have to do to perform the pile shuffle backwards.
But shuffling is not commutative, so if you plan to get a bad deck by doing a reverse pile shuffle, after "pile shuffling then bad shuffling", so have P*B*P^(-1),you won't get B (just bad shuffle).
So why pile shuffling at all? In Dominion, it also has it's merit even if it does not add randomness. This is because you have many similar cards, and usual shuffling techniques will work better if these similar cards are distributed around the deck. See
David desJardins explaining it to Donald:e Forgot the *: Of course just by this it is not entierly clear that the cricle starts at the beginning, this is left as exercise to the reader.