They're doing it by digging and compressing dirt in the process. They are moving as much as possible into the Mariana Trench, but there would still be the issue that the water going into the under-construction tunnel and lowering sea levels noticeably.
To cover this up, they're helping out global warming by encouraging the Chinese to burn more and more oil, which helps melt the polar ice caps and gets the sea level to rise more than it would otherwise be sinking. But not enough!
The following graphs were carefully constructed from data taken from the NFDSK on climate change, conducted on February 30th 2008.
And following is an artists rendering of the tunnel, code name "Han Hole"
If I go missing, then you know that this is true.
UPDATE: The NFSDK is such an ultra-secret organization that they had their entry removed from acronym finder. Go search for it. It's gone.