mdf: TradeMe's TradeRunner product is designed to connect e-commerce and trademe retail channels. Basically you manage product descriptions, pricing and inventory from TradeRunner and it syncs it across your various sales channels. WooCommerce is a listed channel.
ChannelAdvisor will do it too (though for much greater cost).
I found traderunner was quite surprised by the quality of the whole thing for connecting woocommerce to TM I still cant work out how they make money!
I asked if they could go the other way and reply was No