I know i'm late but I'm having the same issue with my 2004 TSX. I'm at 30k and it's been really bothering me. I took it in and they told me it's normal. It wasn't the brakes nor rotors so I don't know what it could be.

 

With just under 2,000 miles on my new '06 I started hearing a groan/grind each time I pressed the accelerator from a stop (whether backing up or driving forward).

Took it to the dealership and went over it with the tech to ensure that he heard the noise I was hearing.

Took them about 45 minutes to figure it out, but seems the the bushing on the subframe bolts was rubbing and needed lubrication.

Hope this helps!

 

Clunking is the ABS selftest. Scraping is not.

For those with scraping and still haven't sent their cars to the dealer, check the dustshield that is behind the brake rotos. It's a thin metal piece. Sometimes when mounting the wheel on the hub, they accidentally brush against the shield, bending it towards to the rotor and scraping it once in a while. If the space between the wheel spokes is large enough just push at the dustshield inwards. Otherwise just take the wheel off and check it.

 

I totally know what you're talking about. My exact situation. When I first got my car, exact same scraping noise. I brought my car in and then they couldn't figure it out and when I got a loaner car, same scraping noise. I just accepted the fact that it scraps.