I think you mean Wonder Cards
>A Wonder Card is sent together with a Mystery Gift, and it usually provides detail for the gift the player has received.
>Wonder Cards contain such information as the name of the bundled gift, whether or not the player has already received the gift before, the in-game event caused by the Pokémon, the date the gift was received in the game, and a brief description of the gift; an icon of the associated Pokémon is also displayed for further identification.
Source: Bulbapedia/ Wonder Cards
Deleting the Wonder Card will not delete the Event Pokemon.