Your not supposed to be encountering the Burnt Offerings cards in the 1st three scenarios, so technically you should remove them, and i would especially if i am introducing the game to other players.
But what I have been doing for solo is just keeping all the cards together, and when I encounter a card with a 1 in the top right corner of the card I just draw a random card from the box, and repeat until i get a B or C. This works fine, and I don't mind it in solo, but I think it would be a bit disruptive to game play with a group.
I use the same method as @Tracker1, but for new players I go through the pain of removing all the (1) cards because I think it would put them off to keep saying 'oh, we can't face that one yet'!
I find that it doesn't take that long to remove the cards. I think it is worth the effort.