This is a very sticky legal area.
1. TSA clerks are not law enforcement, so they have no law enforcement powers.
2. It is further my understanding that, as a matter of agency policy, they are instructed not to detain anyone.
3. As citizens they have the right (subject to state law) to effectuate a citizens arrest of someone committing a crime using (subject to state law) reasonable force. So, for example, if a TSA clerk was in the airport restroom, and witnessed what they believed was an actual rape (a felony in, I believe, every state), they would have the right, as a citizen, to detain the subpect and even use reasonable force to do so. But they might get fired for violating agency policy.
4. Under TSA policy, the RPD is supposed to be in a private room, whether or not you agree. Of course, they can't force you into a private room. And if you refuse then they can all a LEO to assist (not sure what the charge would be), but the LEO almost certainly would not use bodily force to put you into the private room. Even if it proceeded to an arrest, thier "frisk" would be in public and you would be removed from "TSA control" before the TSA got to do a RPD. What does that all mean? Darned if I know.