You won't have any problem travelling to India if you travel with Nepali passport. GC is needed only to travel back to US.
I wonder why would you travel via India if you have Nepali passport. Did you get your status thru Asylum? If so, you need to travel through India or third country and conceal that you visited Nepal. It is because the regulations say that USCIS may retreat or take back your immigration status if it proved that you visited your country.