- Just like with Tears of Lys, Tyene's ability doesn't target (it doesn't have the word "choose"), so it get around immunity and protection from being targeted. Also, the poisoned character is killed "at the end of phase", which happens after the "until the end of phase" lasting effects expire, and outside of the challenges phase, so Winterfell Crypt and Crossroads Sellsword won't trigger.
Note that, unlike Mirri Maz Duur and Dagmer Cleftjaw, Tyene's ability is not a claim replacement effect, but a regular Reaction to winning a challenge (so you get both the poison effect and intrigue claim).
- Multiple poison tokens must saved from separately, because each poison token comes with a separate "kill" effect. So if a character has one poison token from Tears and one from Tyene, that character will need to be saved twice. For example, you could use a duplicate for one poison token and an Iron Mines for the other.