The expression is originally that someone is a nitpicker:
pedantic critic, 1951; see nit (n.) + pick (v.)
Nits are louse eggs (very small things) and someone who picks them is paying (too much) attention to very little things. In a play of words, the expression has been undone into picking nits. Without the pre-existing nitpicker, it wouldn't make much sense.
The "joke" works only based on the reader's knowledge of nitpicking, just like I could have a stab at humour saying that I am cleaning vacuum when I am cleaning the house.
In the context you quoted, it means that the XML tools will take care of all the little details for you (presumably so that you can focus on the bigger, more important things).