I've never tried this on microfiber, but it has worked well on suede leather with grease stains. I got salad dressing on a skirt, and movie popcorn butter on a jacket. Lay the item flat, stain up. Sprinkle talcum powder enough to cover the stain completely. Let sit for at least 24 hours. Take outside. Shake/brush the powder away, and the stain will be much better or gone. Repeat if needed.
My skirt took one treatment, and my jacket took two. You can vacuum the powder up with an upholstery attachment if all the powder does not brush away. I don't know if it will work on your purse, but it might help.
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