Many of us undergo the same "special screening" at every airport security check: for example, checking of CPAP machines for explosives, and a special screening because of a metal bone replacement. The TSA workload could be reduced by creating a document (analgous to a passport) which someone one of these problems could apply for: it would have a photo ID and space for a screener to stamp that they had checked one of these "known problems" and found it to be OK. Screeners should then be given the option of letting a document substitute for the actual check; they could do this, or do the check (and give the stamp). Since it would remain uncertain if you would be checked, there would be little loss of security (even a forgery would be no guarantee). But if screeners had this history to see, they could, in many cases, decide to let someone with a well-stamped document through without the usual extra check.
Why the contribution is important
This would be a small gain for these travellers (they would be like those without special issues, most of the time) and probably a larger one to the speed of screening.