Previously, processors and merchants accepting bitcoin payments would wait until a large fraction of bitcoin nodes listed a 0-conf txn as "valid-but-unconfirmed," the so-called memory pool or mempool (because it is a collection of transactions in RAM). This works well, because we empirically know how nodes operate: they accept these valid-but-unconfirmed txns into the blockchain and reject (both discard and fail to relay) any competing txns ("doublespends"). Doublespend attacks worked by filling the global mempool with the doublespends before the original txn fills the mempool. Naïve software wouldn't check the global mempool. So really, there were two types of 0-confs: txns which were agreed upon by >90% of the global mempool and those which it was unknown (but sometimes assumed).

Now, BitUndo changes how people perceive mining nodes! No longer is the mempool immutable, but rather mutable for a price. This price, as it stands, is 10% per successful undo and 0% per failure. So if BitUndo (and federated pools) controls 1% of the network, then 99% of 0-confs will confirm, 1% will be undone, and 0.1% of the total transferred will be paid in fees to BitUndo. It throws more of a wrench into the system as the BitUndo federation varies from 0% to 100%. Empirically, it will be trivial to see what percentage of the network is engaged in BitUndos. If that percentage becomes materially large, then it will have a material effect on how the system treats 0-confs, for better or worse.

Interesting, this service is definitely available privately (or should be assumed to be). As U.S. Supreme Court Justice Louis Brandeis once said: Sunlight Is the Best Disinfectant