How can I clean grease from a carpet?
First - don't scrub it.  Scrubbing with improper treatment will work the stain further in.  Good news is that oil doesn't dry, so you can get it out. Bad news is that whatever filth is in the oil may set.

(I was curious what regular people do, so this is from Good Housekeeping)

1) Apply an absorbing agent. Baking soda is a good go-to and is relatively cheap. Apply liberally and let sit for 10 minutes. Vacuum it up.

2) Use 1 tbsp vinegar + 1 tbsp hand dishwashing detergent + 2 cups warm water. Sponge the stain and blot till absorbed, repeat as necessary.

3) Sponge with cold water and blot dry to absorb vinegar solution.



However, I have doubts as to the effectiveness of using any solution of mostly water on carpeted oil or grease.  What I would do, and know works, is use odorless mineral spirits to get the stain out.  Any kind of paint thinner will do, but OMS (as the name implies) doesn't have the same smell as others. Whatever OMS is not removed by blotting will quickly evaporate, along with the smell.

If you go the effective OMS route - follow the safety guidelines.  It's flammable until it evaporates.