Wet work

In a recent article in the New York Times this passage occurs: '... the Albanians ... did
wet work for the K.G.B.' Does 'wet work' mean 'dirty work'? If so, why?

It means more than dirty work. "Wet work" is spy slang (and allegedly CIA slang) for missions involving killing someone - also known as "sanctioning" someone. I imagine it's called "wet work" because it sometimes gets a bit messy.

Here's a source:

Wet Work: Western slang for intelligence operation involving murder or assassination. COVERT TERMINOLOGY www.geocities.com/ s75j88w68/covert_speak.html

WET WORK
An operation involving the shedding of blood. KGB term.
[Cf. _Mokryye Dela_, the KGB department of wet work --masakim's note]
From _The Dictionary of Espionage: Spookspeak into English_ by Henry S.A. Becket.

wetwork noun
An espionage assignment that calls for murder.
[From _Wetwrk_, a novel by Christopher Buckley]
From _Trash Cash, Fizzbos, and Flatliners: A Dictionary of Today's Words_ by Sid Lerner et al.

wet-job a murder.
But not necessarily by drowning: "If anyone fancied the idea of doing a 'wet-job' on me then the bomb would go off in hours." (Ted Allbeury, _Pay Any Price_, 1983)
Also as _wet operations_: "Max was an expert at what the chekists tactfully described as mokrie dela, 'wet operations'." (Robert Moss, _Carnival of Space_, 1987)
From _A Dictionary of Euphemisms_ by R.W. Holder