Dilution and adiabatic demagnetization refrigerators based on pulse tube cryocoolers are nowadays used in many low temperature physics experiments, such as atomic force and scanning tunneling microscopy, quantum computing, radiation detectors, and many others. A pulse tube refrigerator greatly simplifies the laboratory activities being a cryogen-free system. The major disadvantage of a pulse tube cooler is the high level of mechanical vibrations at the warm and cold interfaces that could substantially affect the performance of very sensitive cryogenic instruments. In this paper, we describe the performance of a very simple mechanical attenuation system used to eliminate the pulse-tube-induced low frequency noise of the superconducting transition-edge sensors under development for the instruments of the next generation of infra-red and X-ray space observatories.