I'm a little unclear on what happens to cards with this descriptor (like Avatar of the Fallen): it makes sense that they're unaffected by cards that let you banish from the center row, but what happens when they're defeated? Do they stay in the main row? Do they go back in the draw pile?When defeated, you earn the reward printed on them like with any other monster, and then they go to the Void.
Only way to get a card to go back to the Portal deck/draw pile is if you use a Return Of The Fallen exp card that lets you defeat monsters in the Void as if they were in the Center Row. In that case, the card instructs you to place the defeated monster back into the bottom of the Center deck.
This is how I was taught by several groups, but the iOS version of the game also implements it this way.