Travelled to Nepal and back. Here is my experience.
Going to Nepal no issues whatsoever, stayed for 50 days plus.
Coming back via Kathmandu and Doha on Qatar Airways. Immigration officials in Nepal do know TPS, so encountered no problem, but i explained to them about the travel document proactively to avoid any confsuion, had to show work permit and that was it.
Almost same thing in Doha showed Passport and travel document boarded aircraft no issues.
Finally elephant in the room arrived in DFW after long transit and flight. I had decided not to carry any food item just to avoid any possible scrutiny or declaration to customs. I asked and was directed to the line for people with Travel documents. My Fingerprints and picture was taken no question was asked, I was only required to show my AP and passport, officer did not ask for any other paper, then I was sent to second inspection. There were five people ahead of me. I saw a lady behind the counter who looked like she was on some sort of visa of Travel document, she was asked to leave the country within certain date, that made me really nervous including everyone else who were waiting. I did not know her situation, not did I know her visa type or status, so I did not entertain the thought too much althought I felt bad for her and kid.
Officers took their sweet time, some asked question after question to other individuals. Finally they called my name, I was very nervous as I approached the window and officer who called me. As soon as I approached the window he said "you are good to go" he already had stamped my AP and passport. I had forgotten to surrender my I-94 prior to my departure so I asked if I could hand over my old I-94 and he said "no, not necessary". I was out within half hour.
That is the entirety of my experience, hopefully this will help who are thinking of traveling on TPS/AP.
