Serviette

If you are going to eat using your fingers (a very medieval practice), using a serviette (or at a pinch a tea towel), prevents getting nasty hard to remove grease stains on your garb from the roast chicken and making the hospitaller angry if you borrowed the garb.

Serviettes are also a nice place to practise decorative arts such as embroidery, drawn thread work, and needle lace.

The other, and more period option of cleaning your face and removing greasy bits from your hands and mouth is using the tablecloth. Yes - that's what they're there for! Don't be afraid, they're going to get washed anyway.