I find pearls can be very grubby when they are sent to me for restringing! For big bits of make-up or food (yes really) I use a new scalpel blade to gently remove the dirt.
After that I like to wash the whole strand of pearls in a bowl of tepid soapy water(I use grated hand soap NEVER washing soap) after washing gently you need to rinse all the soap off and dry on a clean linen tea towel. When I have dried the pearls I will restring them and finally use my fingers to rub in LUSH lip salve which comes in a flat metal tin.Other organic lip salves or even skin creams will work but nothing tinted or scented with essential oils!
To keep pearls in good condition and to avoid broken thread always put on scent and skin care products BEFORE the pearls!And remove any bit of dried on food or make up.