This looks like oak which has an open grain. Your stain has landed in the grain pores but wiped off the late season wood which leaves a "dramatic" contrast and shows up the marks.
Rather than try to eliminate the stains (crayon or whatever) consider darkening the lighter parts of the table making the stains less obvious
You might try an aniline water stain. This comes as a powder and is completely dissolved in water and will even out the colour. The whole table will be darker depending on the colour of stain and how any coats are applied. Only works if the table has no finish that would have sealed the wood.
The idea is to even out the contrast from the original staining and make the marks less obvious.
After your first sealing coat (I use shellac) you can use an oil stain to touch up any uneven spots. Because the surface is sealed it wont soak in and can be wiped off with a rag dampened with thinner,