Is there any way of get rid of the following text from an empty Gmail inbox;
"No new mail! There's always Google News if you're looking for something to read."
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No way to do it within the available settings (public Gmail and Apps). You'll have to do something client-side (eg via GreaseMonkey).
You can use adblock plus as well. A bit simpler than GreaseMonkey because you just click and block.