What is the ruling on the desecration of the prayer beads? And is it considered an act of disbelief (kufr)?

A rosary (misbaha) has no inherent sanctity. Scholars have differed regarding the ruling on using it for glorification (tasbih). However, if something from the remembrance of Allah or a name glorified by the Shari'ah is written on it, then it is not permissible to treat it with disrespect (imtihan). Deliberately disrespecting it in such a case would be an act of disbelief (kufr) because of what is written on it. As for a rosary devoid of such inscriptions, it does not take the ruling of objects whose disrespect is forbidden.