After I attach and trim, I brush in all directions.
Here's what a piece looks like after trimming and before the lint brush.
And here's what it looks like after I go over it with the lint brush.
I can easily trim those threads now that I can see them.
I keep brushing and trimming until there are no more threads that stick out to be trimmed off. Even then, I'll still have the occasional thread that pokes out where I don't want it. For those, I suggest a permanent marker.