I have two ways of feeding frozen bloodworm. I either throw a frozen block in the water and let the fish attack it. This is great for surface feeders.
Or, I thaw a block out in a cup of tepid water and gently stir it to disentangle the clump as it thaws. Then I throw the cup of water in and this is great for midwater feeders.
I have noticed when doing the latter that there are always bits of bloodworm skins, usually brown with no blood in them. I presume these are the "things" you refer to? To be honest if you went down the route of trying to remove them all you'd be at it for hours with tweezers. It's not worth the hassle to me, the fish just eat the lot anyway.