  We discuss a recipe to produce a lattice construction of fermionic phases of
matter on unoriented manifolds. This is performed by extending the construction
of spin TQFT via the Grassmann integral proposed by Gaiotto and Kapustin, to
the unoriented pin$_\pm$ case. As an application, we construct gapped
boundaries for time-reversal-invariant Gu-Wen fermionic SPT phases. In
addition, we provide a lattice definition of (1+1)d pin$_-$ invertible theory
whose partition function is the Arf-Brown-Kervaire invariant, which generates
the $\mathbb{Z}_8$ classification of (1+1)d topological superconductors. We
also compute the indicator formula of $\mathbb{Z}_{16}$ valued time-reversal
anomaly for (2+1)d pin$_+$ TQFT based on our construction.
