I have Littlefinger (doesn't matter which one) and The Moon Door (A House of Talons). My opponent has The Pleasure Barges (A House of Thorns) and a (non- Army ) House Tyrell character with "cannot be discarded from play". What happens if I try to target this character with The Moon Door's effect?

The Moon Door

Response: After you win a challenge by 4 or more total STR,choose and kneel a non- Army character. If you control The Eyrie or Littlefinger, instead kill that character.

The Pleasure Barges

If a House Tyrell character would be killed, it is instead discarded from play.

They are an eligible target for your effect, so it should go through successfully, so I would think the replacement effect on their Pleasure Barges would fail for that character, as it cannot be discarded and they would simply be killed. It seems to be the same situation as the replacement effect on the Chargendas failing, they simply continue to their original moribund destination.

The more I think about it, the more I think J_Roel is correct. The replacement effect fails to replace "killed" with "discarded" because it cannot be discarded from play.