I recently re-discovered a set (it was hidden behind a bookshelf at my old workplace for seven years!) and noticed this image and text on the lids of the plastic bowls. Does anyone here have enough of a grasp of Chinese / Korean to translate this?

It's probably something along the lines of "Go Stones" but I'd like to know for sure

바둑 is 'baduk', correct? But the first two characters look like Chinese to me.

Yep, 바둑 is 'Baduk'. And '韓' is for 'Korea', and　'一' means 'one'. You can read the whole thing as "Hanil Baduk".
Basically, you have a set of Korean Go stones

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be immersed

Cool, thanks Kirby!

Kirby, could 韓一 or 韓一바둑 be the brand name of this particular Go equipment or manufacturer ?

Yes, there is such a shop, so it's certainly possible. In fact, that's what I originally wrote, but I'm not 100% sure about the details of that company, so I omitted that part.

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be immersed

I remember seeing these plastic bowls around. It looks like Kirby/EdLee are right and it is actually from the Hanil Badook store: http://www.hanilbadook.com/

The exact product can be found under 기타상품 (Other Products) > 바둑통 (Baduk Bowls)

It looks like the artist they hired doesn't really understand how wood works.

yeah, that's caught my eye each time I open the lid -- but drawing the grain "correctly" would have looked weird, and with the awkward perspective it sort of works.

Or maybe I've just become used to it.