Step 1: Recall the accepted criteria for a good screening test.
Public health textbooks list a fixed set of qualities a screening test must have before it is used on a large population. These include validity, meaning good sensitivity and specificity in picking out true cases, reliability or reproducibility, meaning the same result on repeat testing, simplicity, safety, acceptability to the public, low cost, and feasibility, meaning it can actually be carried out on a large scale with the resources at hand.
Step 2: Check validity.
Validity is a core, required criterion, since a screening test that cannot correctly separate diseased from healthy persons is not useful at all.
Step 3: Check reproducibility.
Reproducibility is also a required criterion, a test that gives different results each time it is repeated on the same person cannot be trusted for screening a whole population.
Step 4: Check feasibility.
Feasibility, meaning practicality of applying the test on a large scale within available money, staff, and time, is one of the standard listed criteria for any screening programme, including diabetes screening in people over 40 years.
Step 5: Check ingenuity.
Ingenuity means cleverness or inventiveness of a method. It is not one of the recognized criteria used to judge a screening test, no public health text lists ingenuity as a required property.
Step 6: Final answer.
The property that is NOT a required criterion for a screening test is
\[ \boxed{\text{Ingenuity}} \]