From the Super Mario Wiki, the Mario encyclopedia
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Bonus Cards (originally known as Scratch Cards) are a bonus feature in Mario & Luigi: Bowser's Inside Story and its 3DS remake, Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey. They allow the Mario Bros. or Bowser to get a refund for some of the coins they spent back when shopping. A higher Stache or Horn stat affects the odds of winning. After purchasing something from a shop, the player may be given the option of scratching a card by rubbing a card on the Touch Screen with (selecting a card in the remake). Scratching a Mushroom refunds 10% of coins spent, a Fire Flower refunds 20% of coins spent, and a Super Star refunds 40% of coins spent. However, if the player scratches a Fawful, there is no bonus.
There are three different kinds of scratch cards depending on the Stache and Horn stats. The Stache numbers represent Mario and Luigi's combined numbers for the stat: