Olives in vinegar should only be purchased if Rabbinically approved. Plain olives pickled in brine, acetic or lactic acid are permitted (lactic acid is not obtained from milk). It is advisable to check the ingredients declaration to make sure that non kosher ingredients such as wine vinegar are not included. Kalamata Olives are not permitted as they are normally pickled in wine vinegar during processing.
Olives from small "kitchen" companies such as Belazu/The Fresh Olive Company may be problematic and should not be used. Some of their products do not specify a brand on the front label, but "The Fresh Olive Co Ltd t/a Belazu Ingredient Co" is included in the company details on the back.