The cards can be read through the wallets that are supplied with them, which are quite thin - I've never tried scanning them when they're inside a purse or leather wallet though, and have no idea whether that would work. Nearly everyone seems to keep them in the official Oyster wallets - the original ones have the iconic Oyster design - but if you've bought yours more recently you'll have a minging yellow one and will be advertising for Ikea.

The card readers are on top of the turnstile, so you'd have to be pretty tall to be able to get your pocket near enough to scan without removing the item.