As explained in the Inglorious Basterds screenplay:
DRIVER
Why did you allow a enemy of the state
to escape?
COL LANDA
Oh, I don't think the state is in too
much danger, do you?
DRIVER
I suppose not.
COL LANDA
I'm glad you see it my way. Besides,
not putting a bullet in the back of a
fifteen year old girl, and allowing
her to escape, our not nessessarlly [sic]
the same thing. She's a young girl, no food,
no shelter, no shoes, who's just witnessed
the massacre of her entire family.
She may not survive the night. And after
word spreads about what happened today,
it's highly unlikely she will find any
willing farmers to extend her aid.
If I had to guess her fate, I'd say she'll
probably be turned in by some neighbour.
Or, she'll be spotted by some German
soldier. Or, we'll find her body in the
woods, dead from starvation or exposure.
Or, perhaps-she'll survive. She will
elude capture. She will escape to America.
She will move to New York city.
Where she will be elected, President of
the United States
And in the spirit of the movie, Landa is The Jew Hunter. He's good at what's he's doing, but he also likes it. An escaped jewish girl is another prey for him. So he can hunt a little longer. For me it was part of showing Nazis as not "following orders", but people who are evil on their own. Who find and seek pleasure in tormenting other people.
Quote copied from www.scriptslug.com
