A screenshot likely doesn't tell people anything valuable about the app - it's not visually appealing, details would be infeasibly small on a business card, and a screenshot is impossible to search. As soon as you change the look of your app, all of your existing business cards suddenly have negative value.
Also, you're paying more for higher quality printing, and most people you give these cards too to will wind up forgetting about them or throwing them away. Maybe, instead of a screenshot, consider hiring someone to create a simple infographic better suited to the format, that could communicate the concept more clearly, and look good on less expensive stock.
