In the US, a few national bakeries manufacture whole-wheat pitas that, while not as "neutral" as normal pitas, are more neutral than whole wheat bread.
Whole wheat bread can contain molasses or cane juice in order to mask bitterness, which can give it a strong flavor that's unwelcome. The whole-wheat pitas I've tried don't concern themselves overmuch with bitterness, and use ingredients like oatmeal flour and flax seed to give their product a more neutral taste.
I've got a package of "Joseph's Flax, Oat Bran and Whole Wheat Pitas" in my desk drawer as we speak - the texture is rougher and not as tender as a normal pita, and it's definitely more bitter, but when used as an accompaniment for soups, stews, hummus or grilled meat, it's more than acceptable. Each pita is 50cal, with 7g carbs, so definitely low-carb, but they are not slow-carb, as the main ingredients are wheat gluten and corn starch. The whole-wheat flour, flax seed and oat bran are used for flavor rather than as the main ingredients.