Properties of inductors with a magnetic core
All magnetic materials have a B-H curve as shown below where B is the flux density and H the magnetic field strength.  The effect of permanently magnetising the core is to shift this graph along the H axis.

Note \$ H \$  is the sum of \$ \frac{N \cdot I}{l}\$  where \$ N \$ is the turns of your coil, \$ I \$ current, \$ l\$ magnetic path length and the magnetic field strength from the permanent magnetisation.

The end result being that the inductor will start to saturate at a lower current in one direction and an higher current in the other.  


(source: electronics-tutorials.ws)