Not to worry. There is no internal finish to wear off - it's streaks of copper from the bulles.
Hoppes 9 doesn't remove copper (pretty sure), so some is left behind. You can ignore it or, if it bothers you, switch to a cleaner that does strip copper. I like Shooter's Choice "MC #7 Bore Cleaner and Conditioner". So do benchrest shooters (combining it with Kroil).
After you brush, run rubbing alcohol across the brush to remove the cleaner - otherwise the brush will dissolve - it's copper too. I just hold the brush over a garbage can and trickle alcohol (99%) on to one end, letting it run off the tip carrying debris away.
Hoppes 9 doesn't remove copper (pretty sure), so some is left behind. You can ignore it or, if it bothers you, switch to a cleaner that does strip copper. I like Shooter's Choice "MC #7 Bore Cleaner and Conditioner". So do benchrest shooters (combining it with Kroil).
After you brush, run rubbing alcohol across the brush to remove the cleaner - otherwise the brush will dissolve - it's copper too. I just hold the brush over a garbage can and trickle alcohol (99%) on to one end, letting it run off the tip carrying debris away.