Why is there often a metal clip around a dc motor

The metal has a very high relative permeability. This means that most of the stray magnetic field will go through the metal and not through the surrounding air. The advantage of this is less magnetic field radiation because most of the magnetic flux is confined to the metal. Mu metal is expensive but performs well in this job. These metal covers were common well before EMC regs became an issue. Some circuits get mucked up by stray magnetism; CRTs and Tapes are examples.