A generator of telegraph noise coupled to a conducting channel may fully dephase quantum transport through the latter. Here, I will address the case where a quantum dot (QD), playing the role of a charge fluctuator, is tunnel-coupled to an additional channel. When this additional channel supports a fractional filling factor in the bulk, distinct differences from the integer case arise. Abrupt phase lapses of the transmission through the conducting channel occur. This is accompanied by a cusp-like suppression of the interferometer's visibility, yet no full dephasing. This is to be contrasted with the integer case, where phase lapses are generically absent, and full dephasing is possible. These results are interpreted in terms of the entanglement between the fluctuator and the conducting channel. Experimental implications will be briefly discussed.