As a crucial application in privacy protection, scene text removal (STR) has received amounts of attention in recent years. However, existing approaches coarsely erasing texts from images ignore two important properties: the background texture integrity (BI) and the text erasure exhaustivity (EE). These two properties directly determine the erasure performance, and how to maintain them in a single network is the core problem for STR task. In this paper, we attribute the lack of BI and EE properties to the implicit erasure guidance and imbalanced multi-stage erasure respectively. To improve these two properties, we propose a new ProgrEssively Region-based scene Text eraser (PERT). There are three key contributions in our study. First, a novel explicit erasure guidance is proposed to enhance the BI property. Different from implicit erasure guidance modifying all the pixels in the entire image, our explicit one accurately performs stroke-level modification with only bounding-box level annotations. Second, a new balanced multi-stage erasure is constructed to improve the EE property. By balancing the learning difficulty and network structure among progressive stages, each stage takes an equal step towards the text-erased image to ensure the erasure exhaustivity. Third, we propose two new evaluation metrics called BI-metric and EE-metric, which make up the shortcomings of current evaluation tools in analyzing BI and EE properties. Compared with previous methods, PERT outperforms them by a large margin in both BI-metric ( $\uparrow 6.13$ %) and EE-metric ( $\uparrow 1.9$ %), obtaining SOTA results with high speed (71 FPS) and at least 25% lower parameter complexity. Code will be available at https://github.com/wangyuxin87/PERT.