At any point, you can choose to move a card in your active area to the discard/lost area as appropriate. So, you could choose to lose opposing strike prior to the monster attacking.
Rulebook pg 25: Under both persistent and round bonuses sections there is verbiage noting cards of these types "can be removed from play at any time".
Thanks for the clarification! I've read through the rules a few times and managed to miss that line. Didn't read it carefully enough