  Pipe dreams and bumpless pipe dreams for vexillary permutations are each
known to be in bijection with certain semistandard tableaux via maps due to
Lenart and Weigandt, respectively. Recently, Gao and Huang have defined a
bijection between the former two sets. In this note we show for vexillary
permutations that the Gao-Huang bijection preserves the associated tableaux,
giving a new proof of Lenart's result. Our methods extend to give a recording
tableau for any bumpless pipe dream.
