They are sent to mark "St Valentine's Day" - which gives us Valentine's cards.
By back-formation from the process of sending these cards, two nouns (or one, with two meanings) were formed. A Valentine can be either the recipient of such a card, or an anonymous wish or gift sent on 14 February. Hence Valentine card.
Finally, taking the first of those meanings, people who receive such cards are 'Valentines'. Hence Valentines' cards.
Personally, I'd favour the first form: 'Valentine's cards'. But I wouldn't say that any one of your three options is 'wrong'.
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