The Travelcard discount applies to anyone with a Travelcard for any
zones of any duration as long as it's valid at the time you're making
your journey. Don't expect any additional discount for using Oyster
PAYG though. You used to get a further 20% off for buying a book of 10
tickets so some people making occasional trips have seen quite a price
hike since Oyster PAYG was introduced on Thames Clippers having to pay
£3.55 per journey instead of something like £2.60.