I had this same problem--there is a service bulletin for a worn rubber o-ring in the inlet line for 03-08 V6 Accords that lets air into the system making the
noise--especially when cold. The Honda dealer didn't even know it and first flushed and changed the reservoir and then tried to sell me a new pump.
Only after I showed him the bulletin did they hand me the o-ring and I fixed it myself in twenty minutes. I replaced the o-ring and the noise went away immediately.
The dealership was embarrassed and refunded my money for the flush, but I wonder how many $600 power steering pump replacements they did instead of replacing the 25 cent o-ring.