I have this problem on my Trek 1000. It's an entry level bike. Ithink it has the same rims that you are talking about. I did some research on it and found that it's common on entry level rims and the brake pads that are used. some info recommended a softer brake pad but I never did find the ones that were recommended and eventually gave up and just dig the metal bits out occasionally.

Do some searches on the internet on it. I was surprised by how many people had the same problem but the guys at the shop acted like they never heard of it.

Honestly I think that the best solution is eventually upgrading your wheels and brake pads.