We have investigated the structural properties of a fluid in which particles, interacting via soft potentials, are imbibed into a disordered porous structure built up by soft particles. Using a Gaussian potential for all interactions involved, we determine via Monte Carlo simulations and integral-equation theory the fluid-fluid, fluid-matrix, connected, and blocked structure factors. Within the explored range of state parameters, the fluid-fluid structure factors display a distinct pre-peak, which we identify as a fingerprint of the structure of the matrix. We show that this feature at low wave-vectors arises from contributions of blocked correlations to the fluid-fluid structure factor. We argue that a similar feature may be found also in systems in which particles interact via harshly repulsive potentials. On the other hand, the variation of the main peak of the fluid-fluid structure factor resembles the behaviour of the equilibrium Gaussian core model fluid. In particular, the height of the main peak changes non-monotonically with increasing fluid density at fixed matrix density. Finally, we analyse the effect of a mismatch between the temperature of the fluid and the temperature of the matrix on the structural properties of the system.
