The effect of the presence of a feedback channel on the transmission of information was first considered by Shannon, who showed that the capacity of a memoryless channel is not increased by the existence of a feedback link even if the feedback link is noiseless. Later it was shown that the information on a feedback channel can be used to improve considerably the performance of channel coding. In this work we study the transmission of an information source through a fading channel with feedback, modeled by a finite-state channel in the Gilbert-Elliot sense. We show that by employing the feedback information in the quantizer design for this finite-state channel, one can achieve lower overall distortion compared to the case where feedback is not available. The feedback channel is used to estimate the channel state using a hidden Markov model, and a quantizer matched to the channel state is chosen based on this information.