T3 uptake is a confusing test (especially by its name).   T3 uptake measures the amount of T4 carrying protein that is not carrying T4.  (T4 is NOT a typo).  As a consequence, a low T3 uptake shows that your T4 is running closer to the hyper end of the range than the hypo end.

from Elaine below...hyper forum, works in pathology
T3 uptake is rarely used is because it measures your level of thyroid binding proteins.
T4 and T3 levels measure thyroid hormone that is linked to this protein and also free hormone.
With the uptake test we used to calculate about how much of the thyroid hormone was free.
The tests that were later developed to measure free T4 and free T3 directly are much more accurate.
T3 uptake is only used to tell if the total thyroid hormone levels are falsely high
or falsely low due to the proteins.

However, some doctors still think we measure T3 with this test because of its name.
We use T3 as a reagent in this test, that is, we add T3 to your serum
to see how much of the reagent binds to protein molecules in your serum