OLENNA TYRELL, QUEEN OF THORNS: PULLING WEEDS

If she uses her Ability on an NCU that has had an Ability resolve earlier in the Round, what happens?

If an Ability has already been triggered and resolved (such as a Once-per-game that has already been activated that Round) the effect remains in play.

If Olenna causes a NCU to lose all Abilities but that NCU is Influencing a unit, is the Influence removed?

No, the Influence remains in play but it ceases to have any other effect.