First of all, you need to vacuum the car trunk from inside and it will remove the dirt from the surface. It can also remove a top layer of the grease.
Then you need to use a dishwashing solution to remove the grease as water will not do any help. This solution is easily available in all stores and is designed to strip the surface of grease. Use it for removing stains of your car and got a desired result.
Take a damp piece of cloth dipped into the solution and dab it lightly on the stained area of your car trunk. Do not put more weight on it as it will make the stain spread around and will become hard to remove them completely.
Use a scrub in circular movement in order to reduce or minimize the damage to the fabric. Rubbing it in a horizontal way can damage the fabric easily.
Now take another damp cloth and do the light dabbing again on the surface. It will help you in pulling up the grease stain quite easily.
After lifting off the stains from the surface, dry the trunk by leaving it opened for a couple of hours. Do not use hair dryer as its heat can also damage the surface of fabric.