First, a significant amount of work needs to be built on the “burn” transaction before it is used to claim the coins on the other chain, for the simple reason of avoiding DoS attacks. Then there is a length of time called the quieting period during which the return transaction and associated proofs are published, but not finalized, and anyone else can step forward with a reorg proof and rollback the transaction. Finally, there is a period of time afterwards analogous to the coinbase maturity where the coins are not spendable because a reorg could undo the peg transaction.

So that's three different waiting periods, each of which would probably be in the range of 100 - 144 blocks, if not more. The exact parameters are not set in stone at this moment, but with that in mind we should expect a peg transaction to take at least 2-3 days to fully clear, depending on the final choice of parameters.