The unique asset deck in Mountains of Madness expansion features two cards which only have an effect if you are on the Antarctica Side Board. What if I am playing against an Ancient One from the base game? Should these components be returned to the box in that case?
As long as you are playing with the Antarctica side board, those cards are usable.
From the expansion rules, page 2:
When playing with the Mountains of Madness expansion, add all expansion components to their respective decks or pools of Eldritch Horror components except for the components described below.
[unrelated items skipped]
Shuffle all Unique Assets to create the Unique Asset deck. Place this deck faceup near the Asset deck.
Should these components be returned to the box in that case?
By the rules: No.
By convenience: Yes.
There are absolutely no effects that would allow you to gain either of these cards without the Antarctica board. Whether you leave these in or take them out, it changes absolutely nothing.
(This is not necessarily the case for some other Antarctica-related cards.)