  Buch and Rim\'{a}nyi proved a formula for specializations of double
Grothendieck polynomials based on the Yang-Baxter equation related to the
degenerate Hecke algebra. A geometric proof was found by Yong and Woo by
constructing a Gr\"{o}bner basis for the Kazhdan-Lusztig ideals. In this note,
we give an elementary proof for this formula by using only divided difference
operators.
