Buckmark cleaning question

[FNG19]

I bought a Browning Buckmark about a month ago, and have been religiously cleaning it after every range trip. To protect the outsides of the barrel from damage to the finish, I've started cleaning vertical (smooth finish) portions as well. I'm using Pro-Shot cleanser/lubricant (the pink liquid) on my guns.

The last two times, I've noticed brownish/orangish smudges on the cleaning patches when I wipe down the outside of the barrel, and it seems like it's not getting much better. The dirt/gunk that's causing it doesn't look visible on the exterior of the barrel. Two questions:

1) What is this gunk?
2) How do I get rid of it?

Thanks!

[Twister]

I get the same orange spots when cleaning the barrel of my Mark III. I ponder the same thing.