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The tick could have just as easily been brought in by a person, someone's baggage, or from the OP's baggage after the plane ride. Ticks are very common in some parts of the US and very rare in others. If an area has ticks, dogs are only one transport vehicle for them.
Compensation is not even remotely called for in this case, IMHO. I personally would rather "brave" a chance at a tick than expose myself to the chemicals required for a fumigation.