Let $f:X\rightarrow Y$ be a proper embedding between complex manifolds, then the normal bundle $N$ is complex which is in paticular $\textsf{spin}^c$. Hence we have a Thom isomorphism $$K^{\bullet}(X)\rightarrow K^{\bullet}(N)$$ in topological $K$-theory. We can then define a Gysin-Thom map $f_*:K^{\bullet}(X)\rightarrow K^{\bullet}(Y)$ by tubular neighbourhood theorem.

Does the Gysin map depend on our choice of the Thom class (aka. the $\textsf{spin}^c$ structure on $N$)?