I would soak it first then gently pry the spike plate off. Go slow with the prying and if it looks like the wick is stuck to the coil, use a paper clip or similar to push the wick all the way
through the spike. Then use tweezers with tips that mate well to get a good hold on the wick and gently work it away from the coil. You can then hold the wick over a stove burner with your tweezers or pliers until it's all clean and white again. The wick is made of silica with a little steel mesh "cap" and doesn't burn, so don't worry if you see it turning red, that's just the gunk on the wick burning off. Then rinse the ash off and insert the wick (little cap end first) back into the spike plate. See this
short video for a demonstration of how far to insert the wick.
