The US doesn't impose any restriction on his travel to any country. But his visit to Nepal might prove otherwise for his refugee status.  He can visit India and sneak into Nepal without any stamp or official documentation.  Being a Nepali citizen, he should not have any problem visiting India. And he should be able to come back to US using travel document.

Beware, Indians do like to give Nepali a hard time, it is in their blood, carry some $cash$.