For the past few days, when I start my car and start driving, I begin to hear a scraping noise from the right front end of my 96 accord. When I press the brakes, the noise stops; when I release the brake, the sound returns. It continues for a few minutes, then it stops altogether. It happens just about every time I start my car and begin driving.

Has anyone ever had this issue

 

dirt / junk in on the brake pads.

We had it on the Honda for a few days then it went away.

I just had to pull someone out of a deep mud pit with my 4 wheel drive truck and now I have horrible scrapping and grinding noises from the front brakes.

I haven't driving the truck much since the noise started but I am sure it will go away once I do.

 

x2 on the brakes.

Another possibility, maybe the brake pads are getting worn out?? They have a little metal tab that scrapes against the rotor when the pads wear out. When it just barely begins scraping, it can do some bizarre things, like you're describing. After a few more weeks it'll wear down more & then it'll start screetching when you apply the brakes.