I don’t know if companies like Gibson use a different type, but all the Chinese kits (not just those via Pit Bull) use a binding that cracks on the surface where it’s bent. The smaller the radius of the bend, the more cracks.
If it’s a water-based stain, then scraping the binding will hopefully remove all the marks as they generally sit on the surface. A model kit sprue remover is actually very good for this, though you can make your own scraper from a bit of slotted broom handle, a craft knife/box cutter blade and a nut and bolt.
If it’s a spirit/alcohol-based stain, then this penetrates a lot further due to its lower surface tension. You can try scraping and you might be lucky, but you’ll probably still see it in the cracks as you can’t scrape too much.
You could try rubbing it with an Isopropyl Alcohol (IPA) solution. 70% with water. 100% IPA can attack the binding and make it sticky. But the IPA is going to remove stain from the wood. So mask the wood and be as frugal as you can.
I simply scraped the binding clean on my first build, an ES-3, but I used a water based stain. I ended up painting the binding on my first ES-1 build as I’d used a spirit-based stain.
The best thing is obviously not to get stain on the binding in the first place. It’s why the basic and more comprehensive kit instructions
suggest you start a build diary, as forum members can tell you things like this. Masking tape helps, but you still get seepage at the edges. Putting clear coat on the binding first creates a good barrier and even if the clear coat stains, you can scrape the clear off. Others have used a rubber/based masking liquid. Some may have used wax (though I’m not 100% sure on that).