1 Alice must know her private key, the amount, Bob’s public key and a public key of BitLaundry. Bob may get a separate message from Alice: “I sent you 100 BTC.”, but he cannot find who sent the 100 BTC from the blockexplorer. It seems to work like a deck of cards, when playing poker, but with everyone signing the cards before discarding them. All info is still on the BC, but it is harder to trace.
2If BitLaundry’s escrow service is nonliquid, too few inputs renders poor rearrangements of the transferred BTCs.
3 Keeping the service honest, may generate income to BitLaundry for a long time.
4 BitLaundry may at some time make sort of a rug pull, when the contract is very liquid. Due to the random delay, the randomness can be extended to infinity.
However as time passes, there will be increased possibilities to track every sat back to the origin, if desired.