  Let $S_k(\Gamma^{\mathrm{para}}(N))$ be the space of Siegel paramodular forms
of level $N$ and weight $k$. Let $p\nmid N$ and let $\chi$ be a nontrivial
quadratic Dirichlet character mod $p$. Based on our previous work, we define a
linear twisting map $\mathcal{T}_\chi:S_k(\Gamma^{\mathrm{para}}(N))\rightarrow
S_k(\Gamma^{\mathrm{para}}(Np^4))$. We calculate an explicit expression for
this twist and give the commutation relations of this map with the Hecke
operators and Atkin-Lehner involution for primes $\ell\neq p$.
