We consider the 3D equation u_{yy}= u_{tx} + u_y u_{xx} - u_x u_{xy} and its 2D symmetry reductions: (1) u_{yy} = (u_y + y) u_{xx} - u_{x} u_{xy} - 2 (which is equivalent to the Gibbons-Tsarev equation) and (2) u_{yy} = (u_y + 2x) u_{xx} + (y - u_{x}) u{xy} - u_{x}. Using the corresponding reductions of the known Lax pair for the 3D equation, we describe nonlocal symmetries of (1) and (2) and show that the Lie algebras of these symmetries are isomorphic to the Witt algebra.