We have studied the influence of pitch-jump defects on the existence of defect-localized states in multihelicoidal Bragg fibers with twist defects. We have shown that the total electromagnetic field energy stored in the defect-localized topologically charged modes essentially depends on the pitch jump and rapidly tends to zero as this increases. This can be used to make the defect mode radiate the stored energy. We have also shown that by tuning the magnitude of the pitch mismatch one can control the wavelength at which the maximal localization takes place. Such fine tuning of the pitch jump can in principle be achieved by piezoelectric modulation.