What about the Egyptians, don't they have a claim to their ancient civilization? Keep in mind that their language, culture, & religion is completely different from what it was in the past. Do you realize that the cross on the Greek flag symbolizes eastern orthodox Christianity?
Only the people who descend from the geographical boundaries of the IVC are allowed to claim that civilization as theirs, no other nation or people have any claims to it whatsoever. Modern day Indians do not speak the language of the IVC, as far as I know even the Indus script has not yet been deciphered. Most of the people I know severely doubt that the religion of the IVC was Hinduism. Hinduism itself is a religion with too many diverse viewpoints, & is more like a hybrid of all the beliefs & practices of the Sub-Continent. I am no expert on Hinduism, so if I have made any mistakes, do correct me. I don't know if this is true but I have heard that even a person lacks belief in God may call himself or herself a Hindu.
I know this isn't an extremely reliable source, but it does talk about the religion of the IVC.
PAKISTAN
My idea of who I am is that I am a Pakistani Muslim of Kashmiri ethnicity & that I descend from Indo-Aryans. It's true that Islam is a way of life & being a Muslim means to belong to a spiritual brotherhood referred to as the "Ummah". Unfortunately some have equated the term Muslim as one belonging to a race or ethnicity, & that is completely false. Muslims are the followers of Islam, they aren't a race or ethnicity, anyone on earth can convert to Islam & call himself or herself a Muslim.