If you deleted the card through your operating system, like through Windows, check the place it puts those, like the recycling bin on Windows. A file is only ever permanently deleted by the operating system if it is too big for that location or if that location is emptied by either the user or enough time passing.
If you deleted the card through the game, I'm not sure how it handles that, but still check like above. There is no reset, only starting over. Honestly, I'm not even sure how you managed to delete a character card when it was loaded into the game. With both AI Shoujo and Honey Select 2, it locks the card so you literally aren't supposed to be able to edit it. This should also be preventing deletion. This is why cards you have loaded into an existing game are marked as "registered" or something to that effect. Once you start the tutorial, you've started the game, which requires you to "register" at least one character card.