Easy solution: stitch it visibly into the fabric of your innermost garment. You want the TSA goons to see the dosimeter if it turns a nice bright mutant-alert color.
I think it would be more effective if it were a nice bright mutant-alert color when you exited the scanner and they asked to see under your shirt because an object was detected. :)
It's very easy to get false positives with dosimeters. See http://www.osti.gov/bridge/servlets/purl/515496-YZWUcS/webvi... A nuclear waste disposal facility had 10% of dosimeters falsely trigger each quarter. Eventually they traced the cause to some overhead lights. Different types of dosimeters can be falsely triggered by heat, cold, UV, or solvents.
People at the TSA know this, which is why they banned dosimeters. Even if backscatter machines are perfectly safe, the TSA is big enough that there will be countless false positives.
Enough. Radiation badges are used routinely in hospitals. I assume that there are far more health care workers that handle radiation than there are TSA agents working backscatter machines (but perhaps it is a mistake to underestimate the extent of the TSA waste).
That's not why the TSA banned them. It ruins the security theater illusion and would bring on countless lawsuits.
The real way to end the TSA reign of terror is to force congresspeople, tsa executives and everyone else who wrote themselves into exemption from all scans and gropes - to actually have to go through lines and security theater. Then it would end quickly.
(TSA agents aren't allowed to have one, maybe the brighter ones will start to wonder why.)