Mirror symmetry aims at equivalences of Fukaya categories (A-side) and categories of coherent sheaves (B-side). Deformed mirror symmetry aims at matching deformations of A-side and B-side. In this talk, I explain how to do it in case of mirror symmetry for punctured surfaces. We start by constructing gentle algebras and matrix factorizations, which serve as A-side and B-side. Then we deform gentle algebras and show how to transfer the deformation to the B-side. (2023 PhD thesis, supervised by Raf Bocklandt)