[LM/BM/SS] Pound of Flesh & Choke

A successful Pound of Flesh causes the victim to have all their attacks reduced by 1 for the remainder of the game. But what if that person uses Choke or Choke & Puke on a player. Choke and Choke & Puke automatically make its victim lose 1 point. Until it is broken or released, the victim will continue to lose 1 point on every attacker's turn. But if the attacker is affected by Pound Of Flesh, then does the victim not lose any points at all, making the Choke pointless, or do they still e the 1 point per turn, but not the initial 1 point when the card is first played?

I am asking this because this actually happened when I was playing with my friend, and we weren't sure what to do.

The Choke & Puke is an attack so I don't see why the damage it causes (no matter when) would be exempted from the Pound of Flesh reduction.