If it were me, I'd take everything out of your purse then turn the lining inside out & using an old toothbrush I'd apply baby-bath or baby shampoo (because it rinses out super-easy) or any shampoo or your favorite stain remover (like Goop hand cleaner is good to remove make-up & oil & grease stains) & just put some on of the cleaner on to the toothbrush then scrub only the stain, then rinse with as little water as possible by using a a clean, damp wash cloth...
A second idea, take your purse into a dry-cleaner & ask them what to do.
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