If someone is unconscientious, they're thoughtless and possibly even dishonest. Unconscientious tourists do things like straying off marked trails, defacing monuments with graffiti, stealing hotel towels, and littering.
The adjective unconscientious is the opposite of conscientious, which means "honest and diligent." So a conscientious person will work hard and act thoughtfully, while an unconscientious person acts without thinking about what is right, fair, or appropriate. An unconscientious journalist might write a story without carefully checking her facts, and an unconscientious dog owner lets their badly behaved cocker spaniel run loose around the neighborhood.