When you stain the carpet with ballpoint pen, apply some rubbing alcohol like isopropyl (90%) onto a piece of clean cloth and blot the stain carefully from the outer edge towards the centre. Do not rub the stain as the stain may spread. Repeat the step until no more ink mark can be removed.
Then rinse the carpet by using a clean damp cloth and blot the alcohol residue from the carpet. Rinse the cloth and repeat the step until the alcohol residue is removed from the carpet. Dry the damp carpet quickly to prevent any remaining ink in the carpet fibre from wicking up to the surface of the carpet and become visible again. To quick dry, you can either use a hairdryer or apply some kitchen paper onto the damp carpet and apply pressure to absorb the excess fluid till the carpet is dry.If you stain the carpet with a fountain pen, repeat the above step using soda water instead of alcohol to blot the stain.