The Hebrew letter Chet does indeed correspond to the Arabic letter ح which makes the hard H sound. Since most Hebrew speakers cannot pronounce it, the closest sound to them is KH (also represented by the letter Kuf, Arabic equivalent is خ), thus when they try to pronounce "Hamas", they end up saying "KHAMASSS". And no, Chet is not the only Hebrew letter affected by a sound change like this, but it's the relevant one because it's used in the Hebrew spelling of "Hamas".

Hope that makes it make more sense.