Retinal vessel segmentation has been widely applied in ophthalmic disease diagnosis. However, current deep-learning-based vessel segmentation methods still suffer from disconnected vessel structures. They struggle with noise interference and low signal-to-noise ratios in difficult-to-separate regions. We typically set fixed threshold values for class probabilities output by the network to separate the results, but this can lead to ignoring vessels in ambiguous regions. Furthermore, current threshold selection methods do not take into account the overall distribution of the sample population. To address these issues, we propose a plug-and-play vessel segmentation reconstruction network, ConformalRefiner, which employs Conformal Risk Control. Firstly, we use a threshold calibration method based on conformal risk control theory to alleviate the uncertainty in selecting an initial threshold, thereby obtaining a significant threshold value that includes more challenging vessels in the calibrated result. Additionally, we design a dual-input reconstruction network that utilizes topological calibration outcomes to guide the reconstruction of the initial segmentation mask. Finally, to tackle the issue of noise introduced by the calibration, we employ vascular topology priors to further enhance performance. Experimental results show our approach outperforms state-of-the-art methods on DRIVE and FIVE datasets, especially in topological connectivity metrics.