Recently Sarkar defined maps for the combinatorial version of knot Floer homology (HFK) whose underlying grid maps could be viewed as births, deaths and saddles. Juhasz has shown that the hat version of HFK is functorial with respect to smooth decorated cobordisms. This leads one to ask the question, "Do these grid diagram maps induce maps on HFK that are invariant with respect to smooth marked isotopy classes of surfaces?" In this talk I will discuss and provide the necessary topological constructions to make sense of this question. Specifically, I will introduce grid movies and show how they correspond to smooth embedded surfaces and I will generalize Carter and Saito's movie move theorem: to grid movies; smooth marked movies; and grid marked movies. If there is time, I will briefly sketch some of the necessary steps to answer the motivating question in the affirmative.