Apparently, this pigmentation fades eventually. You can help it along with nourishing creams/oils like pure Vitamin E.

I have also heard that Turmeric powder/oil fades pigmentation. I havent tried it myself. Mixing turmeric powder with lemon and applying it like a mask every morning is supposed to lighten the pigmentation. Be careful, too much turmeric can discolour your skin and make it yellow/orange. In this case, milk is able to wash it off.

Google it and you'll find lots of different ways of using turmeric powder.