How do you remove oil-based wood stain from wood stairs?
To remove a paint or stain from any surface you should find on the product label what is supposed to be used to thin the product, which in turn can remove the product. In your case since it is oil based you should use mineral spirits(paint thinner) test in an inconspicuous area of the carpet to make sure it does not bleach the carpet and wash with soap and warm water after removal.