No you don't need to take him out. I use Nature's Best bark ( difference from Reptibark is Natures is heat treated to kill any unwanted bugs) since I got my bp which has been a little over 2 yrs.
If they swallow a pc of bark it will not hurt them. They will digest it. Mine has swallowed a bit from time to time. But you should always watch while they eat as mine did get a pc of bark stuck side ways in his mouth that he couldn't shake so I had to pluck it out for him. But no matter what you use you should always keep an eye on them while they eat.
Hope this helps!