you can try taking the white knob off and using some vise grip to get it to move back and forth . other than that what i do is disconnect the heater hoses/controls and remove the heater box. then you can take a wooden dowel and stick it in the bottom hose opening and tap the valve out to clean and reassemble. there is one little very tiny screw that holds the valve in.
or the core will come out leaving the heater box in. the face on the box has 3 clips. also remove the hoses and duct boot.