When you get a passenger that doesn't like to be scanned, you should treat the mission like smuggling: spit chaft and stay in silent mode. Drop a heat sink if necessary. The time you take to scan a beacon or get into a station is quite short, so you can be in silent running with no problem.
I noticed that when I'm carrying passengers, I get scanned much more frequently. And also...boosting away doesn't seem to work that well any more.
So, as a general rule, you want to PREVENT being scanned, as getting away from an initiated scan may get you in other trouble.
To prevent scans: spit chaft often and stay in silent running (it's supposed to make it hard for systems to target you).
To escape an initiated scan:
- boost away (as Serpentis said);
- target the one who scans you and take out your weapons (also as Serpentis recommended);
- if you're entering a station, go through the mail slot fast; it will stop the scan as soon as you're in; however, lately I noticed scans that I escape like this, get finished when I get back out of the station; don't know if it's a bug or not.
In any case, there is no bullet proof solution.