A reader writes:
It may not be fully clear from the post at Gizmodo, but that item was produced as part of an ongoing PR campaign to draw consumer attention to environmental problems. (The tag attached to her bottoms says "[say] no to bags at the cash register.")
Over the past few years there has been a national effort in Japan to reduce the number of shopping bags distributed at retailers to cut down on pollution. The point they're trying to make is that people needn't mindlessly rely on store-provided bags when shopping. You can do your part by employing reusable carrying devices, such as those made from cloth.
Because Triumph is primarily a bra manufacturer, they're making the point using their particular expertise. Since 1997, they have produced four such attention-grabbing items (more important for creating buzz than generating actual sales of the bras) all have been meant to focus consumers on the environment. Culturally speaking, wrapping is a very important part of Japanese gifting culture which has carried over into packaging and bagging at retail. This is a part of a conscious effort to encourage more earth friendly consumption.