Parity is the transformation that makes $x\to-x$, $y\to-y$ and $z\to-z$, so the gradient changes as
$$
\nabla=\left(\frac{\partial}{\partial x},\frac{\partial}{\partial y},\frac{\partial}{\partial z}\right)\to-\nabla=\left(\frac{\partial}{\partial (-x)},\frac{\partial}{\partial (-y)},\frac{\partial}{\partial (-z)}\right).
$$

 Then, since the momentum operator in coordinate representation is
$$
\hat{P}\psi(x,y,z)=-i\hbar\nabla\psi
$$

the parity transformation on the momentum changes it to $\hat{P}\to-\hat{P}\sim-i\hbar(-\nabla)$.