We propose a modification to the TumbleBit protocol, the off-chain payment hub enabling anonymous transactions among users in the Bitcoin network. Specifically, we modify the first step of the protocol by making the tumbler node sending a P2SH transaction onthe blockchain claiming that any user can redeem 1 Bitcoin by providing a SHA-2 preimage of a value chosen by the Tumbler. We remark that our modification enables Bob to transfer its Bitcoin to a third user, and argue that this modified TumbleBit protocol could find applications in permissioned blockchains, for example in the context of anonymous payments between different banks or fintech companies.