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First check your garment's label to ensure that it is washable. If it is dry-clean only, you will need to have it professionally cleaned. If it is washable, you should be able to remove the mayonnaise stain by rubbing the stain with liquid dishwashing detergent designed to cut grease, or with waterless mechanic's soap from an auto parts store, then launder as usual.
A tip I learned from my grandmother was to rub talcum or baby powder on the stain and let it sit overnight. In the morning, brush off the powder with a soft brush or towel. Sometimes more than one treatment is needed, but it almost always works. We never travel without it as it's great for use on my husband's ties.