The petition is to protect the ability of those who would like to say "GOD"-gasp!
It's to stop the leftist radicals from suing states to remove "In God We Trust" from buildings and currency.
It's about giving those with faith equal rights and protections from those who wish to secularize American culture.
If you don't like "One nation, under God", don't say it. But is it worth suing over?

What is unconstitutional about the word "God"?
It does not sponsor any specified God. Could be The God of the Bible. Could be the God of the Torah. Could be Allah, who is claimed to be God. Could be money, as there are many who worship it. Could be Vishnu, one of many Hindu gods.