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Is the "symbol" still a bitmap? I can't read the screen info on the screenshot.
If it is a bitmap, you will need to trace it first and make it into a vector. (that is unless you want to send it to Photoshop and change the colors there, but it still needs to be converted) Once you get it traced..expand appearance and you can then change the fill colors.
right click the symbol and select Break link To Symbol then it becomes an independent shape and not an instance of a symbol in the library. Enabling you to edit colour and strokes also edit individual elements of the symbol.
It appears that you placed an image into Illustrator. If that is the case you need to use image trace, then you can manipulate it as you wish.
I gave him the answer. From his ai file: