How to take care of my satin hair accessory?

Spread baby powder or fine China clay over the greasy stains. Then take a white sheet of absorbing paper, place it over the spot and gently press the low-heated iron over the flat parts to absorb the grease.

You might also use turpentine over a clean cloth (make sure to squeeze the cloth after soaking it with turpentine to get rid of any excess).