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.