Are there any cards in Yu-Gi-Oh that let me interact with face-down banished cards?
There are a few cards that allow you to put these back in the graveyard or deck.
E.g. "Psyframelord Omega" and "Necroface".

The rule around this is that you cannot use cards that limit you to a certain card type (for example 'escape from the different dimension' can only summon back a monster).
The cards I gave as an example do not have these limitations but can put back any type of card, so they still work with face down cards.
Of note is, you yourself can still look at these cards, so you do not have to pick them blindly to put back in the graveyard/deck