After surgical removal of an infected gallbladder, a person must be especially careful to restrict dietary intake of

They must restrict their daily intake of fat and lipids,
gall bladder is a place to store bile, which is produced by liver.
bile can emulsify (physical digest) fats and lipids into numerous oil droplets , to increase the surface area for chemical digestion of fats.
Fat can only be chemical digested by the small intestine, so without the function of bile, fat is a lot of harder to chemical digest. 
therefore, if the gallbladder is removed, they must restrict their diet intake of fats (lipids)