@Usboro: in your case, unless you have US citizenship, even with Greed Card, you are still a Nepalese citizen, and the only passport you can have is a Nepalese passport. So, there will not be any question from US immigration officer or anyone as to 'Nepali Passport kina banayako bhanera sodcha ki vanera ho'..... you're a Nepali citizen, Nepal ko passport nabanayera kaha ko passport bahaune ta.....

@Khoosbu: even though you have obtained your Green Card through asylum, you can legally travel to India. There should not be any issues at port of entry while returning from India visit for a Green Card holder based on asylum approval. The only restriction, I am sure which you are aware of, is not to visit Nepal. However, if you're still concerned be prepared with explanation like - the purpose of your India trip (like visiting different places, visiting friends/family), where did you stay (hotel info etc.), pictures from India trip, or any documentation/receipts/reservations related to your trip - just in case you're asked casually by an immigration officer at port of entry.

Good Luck.