
The advice from today is not to pull out the splinters when you see them because you may make the shinai weaker in that area, it's better to shave them and you should do that carefully because you don't want to shave too much - in the place where the splinter is or when you get resistance when shaving. And the shaving must be done in the direction of the splinter not the other way around (you don't want to get out a bigger piece than it's necessary).
If it's hard to take out the tsuka from the shinai you can use a rubber piece or rubber gloves to ease the action.