We perform collisionless N-body simulations to investigate the evolution of the structural and kinematical properties of simulated thick disks induced by the growth of an embedded thin disk. The thick disks used in the present study originate from cosmologically-common 5:1 encounters between initially-thin primary disk galaxies and infalling satellites. The growing thin disks are modeled as static gravitational potentials and we explore a variety of growing-disk parameters that are likely to influence the response of thick disks. We find that the final thick-disk properties depend strongly on the total mass and radial scale-length of the growing thin disk, and much less sensitively on its growth timescale and vertical scale-height as well as the initial sense of thick-disk rotation. Overall, the growth of an embedded thin disk can cause a substantial contraction in both the radial and vertical direction, resulting in a significant decrease in the scale-lengths and scale-heights of thick disks. Kinematically, a growing thin disk can induce a notable increase in the mean rotation and velocity dispersions of thick-disk stars. We conclude that the reformation of a thin disk via gas accretion may play a significant role in setting the structure and kinematics of thick disks, and thus it is an important ingredient in models of thick-disk formation.