  Recent work of Pechenik, Speyer, and Weigandt proved a formula for the degree
of any Grothendieck polynomial. A distinct formula for the degree of vexillary
Grothendieck polynomials was proven by Rajchgot, Robichaux, and Weigandt. We
give a new proof of Pechenik, Speyer, and Weigandt's formula in the special
case of vexillary permutations and characterize the set of bumpless pipe dreams
which contribute maximal degree terms to the Grothendieck polynomial in this
case. Furthermore, we use this characterization to draw connections between the
Pechenik-Speyer-Weigandt and Rajchgot-Robichaux-Weigandt formulas. We also use
bumpless pipe dreams to prove new results about the support of vexillary
Grothendieck polynomials, addressing special cases of conjectures of
M\'esz\'aros, Setiabrata, and St. Dizier.
