Ballpoint pen ink stains can be cleaned, but they take a long time to clean up. Here's how it is done:

You need to put a clean cloth, I usually use paper towel, behind the stain if you can.

Pour a small amount of rubbing alcohol onto the stain and then blot the stain with another clean cloth like a paper towel.

The key is to blot. NEVER rub the stain.

Also, once the cloth (front or back) gets saturated, you need to switch to a new dry cloth otherwise the ink will not get drawn up when you blot.

You'll find that this take a long time and a lot of blotting. Keep adding alcohol to keep the stain wet and keep blotting. I use paper towels for blotting because you need a lot of towels to get the stain completely up.

It can take up to an hour to get a ballpoint pen ink stain out this way. But it will work.