nothing happens unless you havent picked up what you got from the green guy at the PokeMart.
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As long as you have received the respective Pokémon or item from the green guy in the PokéMart then trashing the Wonder Card will have no side effects to your game meaning if you have received the Secret Key, Oak's Letter or Pokémon Battle Revolution's Magmortar from Wi-Fi Mystery Gift or Wireless Mystery Gift and have already picked it up from the green guy in the PokéMart then it'll stay in your bag no matter what happens to its respective Wonder Card however the item or the Pokémon will be lost if you trash the Wonder Card without first picking up the event from the green guy in any PokéMart.
Im not sure if you ment 'wonder cards' or 'wonder guards', but a wonder guard is when Pokemon can only get hit with super efffective moves such as sheer cold.
You can only send Wonder Cards over to another game if they're programmed to be sent over otherwise you can't send them over.
You are able to get them online to obtain Darkrai.
you have to to obtain the Pokemon and delete the wonder card