No. Only the pump that comes with the bottle of SimplyThick EasyMix will work properly. Old pumps purchased from SimplyThick will not fit on the new bottles. Also, the old pump is not calibrated for the new gel's concentration.
If you decide to use your own pump or re-use an old SimplyThick pump, you assume all risk and responsibility for the condition and cleanliness of the pump as well as the quantity dispersed.
All directions that refer to "strokes" refer to a pump stroke that delivers .2 oz. or 6g or .2mL or 1 mounded Tsp.