The agile Earth observation satellite scheduling problem (AEOSSP) with time-dependent transition time is a combinatorial optimization challenge. Due to its NP-hardness, problem-tailored methods are sensitive to instances and require massive computational overhead. Recently, deep reinforcement learning (DRL) models have shown promise in efficiently addressing the AEOSSP. However, these models may make decision mistakes in specific scenarios due to prioritizing maximizing average reward expectation over individual decision accuracy during DRL training, directly leading to resource wastage. To address these issues, we propose a reconstruction model (RCM), which is a DRL-based two-stage construction model (CM), including a CM and a reconstruction mechanism (RM). RCM constructs solutions initially using a DRL-trained CM, which are subsequently refined by RM. CM utilizes a more efficient network for policy representation to make decisions. RM applies two operators, "repair" and "removal," with a "repair-removal-repair" solution reconstruction process to identify and rectify decision mistakes from CM, offering a modular component to enhance the stability and solution quality. Experimental results demonstrate that the proposed RCM outperforms the state-of-the-art AEOSSP iterative search method, achieving such performance within a computational time of 0.1 s. Additionally, CM surpasses the state-of-the-art DRL policy model and RM can effectively rectify decision errors or suboptimalities, underscoring its effectiveness in enhancing DRL outcomes.