Measurements of the elliptic ($v_2$) and triangular ($v_3$) azimuthal anisotropy coefficients are presented for Image 1 mesons produced in Image 2 hadron decays (nonprompt Image 1 mesons) in lead-lead collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\text{TeV}$. The results are compared with previously published charm meson anisotropies measured using prompt Image 1 mesons. The data were collected with the CMS detector in 2018 with an integrated luminosity of 0.58${\text{nb}}^{-1}$. Azimuthal anisotropy is sensitive to the interactions of quarks with the hot and dense medium created in heavy ion collisions. Comparing results for prompt and nonprompt Image 1 mesons can assist in understanding the mass dependence of these interactions. The nonprompt results show lower magnitudes of $v_2$ and $v_3$ and weaker dependences on the meson transverse momentum and collision centrality than those found for prompt Image 1 mesons. The results are in agreement with theoretical predictions that include a mass dependence in the interactions of quarks with the medium.