Interference alignment (IA) is a joint-transmission technique that achieves the capacity of the interference channel for high signal-to-noise ratios (SNRs). However, most prior works on IA are based on the impractical assumption that perfect and global channel-state information(CSI) is available at all transmitters, resulting in overwhelming feedback overhead. To substantially suppress the feedback overhead, this paper proposes an efficient design of the feedback framework for IA in the K-user multiple-input multiple-output (MIMO) interference channel. The proposed feedback topology supports sequential CSI exchange (feedback and feedforward) between transmitters and receivers and reduces the feedback overhead from a cubic function of K to a linear one, compared to conventional feedback approaches. Given the proposed feedback topology, we consider the limited feedback channel from the receivers to corresponding interferers and analyze the effect of quantization error which generates the residual interference. Also, an efficient feedbackbit allocation algorithm that minimizes the upper-bound of sum residual interference is proposed.