We investigate how small a co-propagating transverse-scalar component can be resolved by Taiji in an already identified bright tensor chirp. Using a source-tracked tensor-null response, we formulate the problem in terms of the minimum resolvable scalar strain fraction and evaluate it over the sky. For a one-year benchmark chirp with tensor signal-to-noise ratio _T = 1000, we find that Taiji can rule out transverse-scalar strain fractions b % at the all-sky median level. The threshold scales as {b,min} _T^{-1}, so brighter tensor events can probe correspondingly smaller scalar fractions. We further find that this sub-percent resolving power remains predictable under small source-parameter mismatches through the associated tensor-leakage structure.