Gritty doesn't equate to obscene - it's referencing that it's more swords-n-sorcery than high fantasy. There are times that punches aren't pulled with things that happen to the characters but they aren't described in a graphic manner.
They're great books, IMO.
That having been said, the book that sets up the second series, Sanctuary can be somewhat disturbing. The book recounts through historical perspective and character flashbacks what life in the city is like when it's ruled by evil cultists. Again, most of the description leaves it to the reader's imagination to fill in the horror aspect. It's more of a "oh wow, that's horrible" than a gross-out, though, so I think you'd be fine.
And a lot of the stories aren't bad at all. They're more day-in-the-life type stories.
Nutshell summary, they're gritty because they're often about surviving physical, magical, and even mundane threats, not because of over-the-top depictions of gore.
Azgulor