Honestly, i think it should be fine. I am working for a direct employer so it was little easier to explain that to the interviewer. I was back there around 6 months back. Luckily, the interviewer also was from the same city where I work, so we got to chat about his hometown for a while. In your case, I think one layer of client and consulting firm between shouldn't be a big deal. One thing, would be to do a mock interview to write down all the possible interview questions about your employer etc. and how you work situation is. They don't have much reason to deny if they don't see any misuse of the H-1B visa like underpaid etc in your case. I've seen people with multiple clients liked Hired by A. (H-1B sponsor), contracted to B, and working at C. That might be bit tricky to explain