This most likely isn’t surface dirt or something you can clean off. CPL filters are built from multiple layers, and if the damage looks like it’s inside the glass, the filter is probably delaminating—the internal layers are separating.

That kind of damage is generally not reversible and isn’t practical to repair. Even if repair were possible, it would usually cost more than replacing the filter.

So the best course is to replace it. If you want to confirm before discarding it, inspect both outer surfaces carefully and see whether the marks stay visible no matter how you clean the exterior; if so, internal separation is the likely cause.