What is the ruling on buying and owning gold-plated playing cards (the deck) with the intention of collecting them as a hobby, and not for eating, wearing, or showing off, and is it obligatory to return them, sell them, or throw them away?

It is not permissible to use paper coated with gold (gilded) if the coating yields gold when exposed to fire. This is due to the generality of the evidence prohibiting gold for men, and whatever is forbidden to use is forbidden to possess. One must repent from possessing it and dispose of it through a legitimate means, such as selling it and benefiting from its price. It is not permissible to give it to someone who would use it in the same prohibited manner. However, if the coating is minimal such that it does not yield gold, then there is no harm in possessing it, unless it is prohibited for another reason.