Baxterization of solutions to reflection equation with Hecke R-matrix

Let $R$ be a Hecke solution to the Yang-Baxter equation and $K$ be a reflection equation matrix with coefficients in an associative algebra $\text{A}$. Let $R(x)$ be the baxterization of $R$ and suppose that $K$ satisfies a polynomial equation with coefficients in the center of $\text{A}$. We construct solutions to the reflection equation with spectral parameter relative to $R(x)$, in the form of polynomials in $K$.