Grid diagrams and Manolescu's unoriented skein exact triangle for knot Floer homology

We rederive Manolescu's unoriented skein exact triangle for knot Floer homology over F-2 combinatorially using grid diagrams, and extend it to the case with Z coefficients by sign refinements. Iteration of the triangle gives a cube of resolutions that converges to the knot Floer homology of an oriented link. Finally, we reestablish the homological sigma-thinness of quasialternating links.