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"Your checked bags could be hit with up to 300mR of X-rays by the new CTX series luggage scanners. " ... from http://home.kc.rr.com/aaronphoto/xray.html

That's not really a major amount.

"The average exposure for Americans is about 360 mrem (3.6 mSv) per year, 81 percent of which comes from natural sources of radiation." http://www.nrc.gov/reading-rm/doc-collections/fact-sheets/bio-effects-radiation.html (sounds right to me... I work with radiation a bit, so I've some expertise... 300mrem/yr natural dose sounds good. Pilots subject themselves to on that order additional cosmic radiation per year, too)

This is about the same as having the kid live in the eastern Rockies for 5 years, where everyone gets on the order of 50mrem /year (Denver,CO) more natural radiation from cosmic rays. If you were to get dose of 30,000mrem, it is possible that a sophisticated blood test could detect that you were exposed to radiation. (Radiation workers in the US seldom get 100mrem/yr above background), but radiation sickness requires about double that dose to be in evidence.

Using worst case assumptions, it appears that the chances of this kid suffering from any long term enhancement in cancer and such risks amount to under 1 in 100... and since the likelihood of cancer resulting from natural radiation exposure appears to be on the order of somewhat under 1%, that means the kid's chances of this would be about 1.01%
... (I suspect living with someone who doesn't speak English is correlated with a far greater enhancement for risk of premature death)

Another useful comparison: a dental XRay is about 150mrem...

--(Radiation workers in the US seldom get 100mrem/yr above background), but radiation sickness requires about double that dose to be in evidence.--

Radiation sickness requires about 500 times that amount and in a much shorter (acute dose) time period.