Plucking them out with tweesers is a stressful buisness for the fish and can leave the fish vunerable to infections. A far less stressful way to completely get rid of external parasites/worms like these is to treat the tank with an anti external parasite med like the one done by Jungle Guard, which will completely eradicate the parasites from the tank with a few treatments.
Edit: By the way, to make sure we are certain of what you are treating, these are what anchor worms look like (in the pic below they are on a small tropical fish called a betta);
i dont think its ancor worns. because the strands are really tiny, and some of the fish just look like a scale or two came off maybe its a bacteria infection but im not sure.