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I don't recognise it (though, that's not surprising given I don't watch much anime). However, looking at the scene and that they're switching between a series of Earth shows (anime, singing contest, weather segment, older black-and-white show, cooking show and finally infomercial) and the all the others are in the same style as the film, it's seems possible the anime scene is also one the filmmakers made themselves rather than took from a genuine anime.
I found the scene on Daily Motion here at 13:44
(I don't know if you can make a link to a point in time on Daily Motion like you can on YouTube). If it is a real anime, it's relatively modern. The girl is using a modern looking smartphone.
The video works fine for me, but there may be a geographical restriction on it. As an alternative, here
is a GIF of the scene.
I'm almost positive that's just original animation created for the movie. The art style and shading scream "western animator imitating an anime style" and doesn't look anything like an actual Japanese production.
Edited by ninjamitsuki2 Call me "Heruru Meruru". http://blue-star-above-me.tumblr.com/

If you have seen Luis and the Aliens, early into the movie there is a scene onboard the alien mothership where the aliens watch Earth tv broadcast and for a "blink-and-you'll-miss-it" moment there is a scene from some anime* on the tv screen, before the aliens switch the channel. Anybody knows what anime is the screen from?