  Continuing previous work, this paper provides maximal characterizations of
anisotropic Triebel-Lizorkin spaces $\dot{\mathbf{F}}^{\alpha}_{p,q}$ for the
endpoint case of $p = \infty$ and the full scale of parameters $\alpha \in
\mathbb{R}$ and $q \in (0,\infty]$. In particular, a Peetre-type
characterization of the anisotropic Besov space
$\dot{\mathbf{B}}^{\alpha}_{\infty,\infty} =
\dot{\mathbf{F}}^{\alpha}_{\infty,\infty}$ is obtained. As a consequence, it is
shown that there exist dual molecular frames and Riesz sequences in
$\dot{\mathbf{F}}^{\alpha}_{\infty,q}$.
