Shroud of Decay

Shroud of Decay
OBL Remove 7 cards in your prey’s ash heap from the game to burn 3 of their pool.

I’m pretty sure the acting methuselah chooses what cards are removed, but I’m not that sure when exactly? During the action resolution or when declaring the action (as you always have to if a card is not explicit - eg Liquidation, “top 7 cards”
Thanks.