We propose a mechanism, through which the low membrane bending rigidity changes the steric polymer repulsion between polymer-grafted bilayers. We calculate the energy of a polymer chain trapped between two thermally undulating surfaces. The proposed treatment is in terms of de Gennes' theory of fluctuations in liquid crystals, later developed by Helfrich for membranes. We show that the confinement energy of the polymer increases due to membrane fluctuations. Also, the repulsive forces between soft polymer-grafted bilayers can extend further from the surface than the height of the polymer layer.