Breach plugs that use tungsten bushings are normally cleaned without removing the bushing. Just clean out you flash channel like you normally would with the proper size drill bit.

The bushing is somewhat of a press fit and won't come out without a little effort. So its best to leave them alone. Bestill has put over 1000 BH209 shots through his rifles he shot at Friendship with no issues. His BH209 loads are far hotter than most peoples.