For the last 10 years I've kept a small bar of hand soap* in my c/o, that's approx. 200 tsa (precheck) interactions as well as several at LHR, never been an issue except ONCE at JFK T4 it was "flagged": "is this soap", me:"yes", them: "OK", JFK T2, T4 and T8 every now and then has TSA who have not been trained properly.
*I once arrived late at night in my booked hotel, the room had NO soap.