Despite their name, chalk pens do not clean off all chalkboard-painted surfaces easily. Pigments in the chalk pens do not wipe away as readily as the pigments in regular chalk, so you may need to use a window cleaner or a melamine foam eraser to get the marks off completely. Check the pen or the pen manufacturer's website if possible, as not all chalk pens are made with the same materials. Some require wet-based cleaning.
Chalk Pens Versus Chalk
Many chalk pens and chalk markers feature "wet" tips, making them more similar to felt-tip markers than they are to regular chalk. Some chalk pens also include richer pigments than standard chalks, which makes them a bit more difficult to erase from some surfaces. Chalk pens are designed for nonporous surfaces, such as glass, metal and glazed ceramics; some are not designed for use on chalkboard-painted surfaces at all. Regular chalk generally won't write on the same completely smooth, nonporous surfaces.
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The Cleanup Process
Wet a lint-free white cloth with a dedicated chalkboard cleaner or glass cleaner. You can use glass-cleaning wet wipes in place of the cloth and liquid glass cleaner.
Wipe the inked areas with the damp cloth, applying gentle pressure. Allow the area to dry completely before writing on it again.
Remove residual chalk ink by rubbing the stained areas with a melamine foam eraser. Wet a corner of the eraser, wringing out excess water, and then gently rub the chalk ink residue. Do not apply firm pressure or it may remove some of the chalkboard paint. Allow the area to dry completely.
Reseason the cleaned chalkboard after it dries by rubbing a piece of white chalkboard chalk over the entire surface. Rub the side of the chalk, rather than the tip, over the chalkboard to cover a larger area at once. Wipe the chalk away afterward with a slightly damp cloth.